diff --git a/jax/_src/core.py b/jax/_src/core.py
index 2dded18dacbc..fd108f372906 100644
--- a/jax/_src/core.py
+++ b/jax/_src/core.py
@@ -3462,19 +3462,7 @@ def write(v: Var, a: AvalQDD) -> None:
                              f"Equation effects: {eqn.effects}. "
                              f"Inferred effects: {eqn_effects}")
       for eff in eqn.effects:
-        if isinstance(eff, effects.JaxprInputEffect):
-          eqn_invar = eqn.invars[eff.input_index]
-          if type(eqn_invar) is Literal or eqn_invar in mut_arrays:
-            continue
-          if (jaxpr_index := in_idx.get(eqn_invar, sentinel)) is sentinel:
-            raise JaxprTypeError(
-                "Invalid `JaxprInputEffect`: must correspond to a jaxpr invar")
-          jaxpr_effect = eff.replace(input_index=jaxpr_index)
-          if jaxpr_effect not in jaxpr.effects:
-            raise JaxprTypeError(
-                "Invalid `JaxprInputEffect`: must be present in jaxpr. "
-                f"{jaxpr_effect} is not in {jaxpr.effects}.")
-        elif isinstance(eff, NamedAxisEffect):
+        if isinstance(eff, NamedAxisEffect):
           # It is valid for a primitive to discharge the named axis effect.
           continue
         elif eff not in jaxpr.effects:
@@ -3604,13 +3592,7 @@ def substitute(aval: AbstractValue):
                                    if type(d) is Var else d for d in a.shape))
               if type(a) is DShapedArray else a for a in out_avals]
 
-  # jaxpr input effects are indexed to include jaxpr.constvars, but the eqn
-  # should have effects indexed only on its explicit arguments
-  effs = {e.replace(input_index=e.input_index - len(call_jaxpr.constvars))
-          if isinstance(e, effects.JaxprInputEffect)
-          else e for e in call_jaxpr.effects}
-
-  return out_type, effs
+  return out_type, call_jaxpr.effects
 
 def _check_map(ctx_factory, prim, in_avals, params):
   if "call_jaxpr" not in params:
diff --git a/jax/_src/effects.py b/jax/_src/effects.py
index efbf10638cf0..b840c934af7a 100644
--- a/jax/_src/effects.py
+++ b/jax/_src/effects.py
@@ -53,7 +53,6 @@
 from __future__ import annotations
 
 from collections.abc import Iterable, Set
-from typing import Any
 
 
 class Effect:
@@ -66,29 +65,18 @@ class JaxprInputEffect(Effect):
 
   This is used as a base class for effects associated with inputs, e.g.,
   reading/writing from mutable inputs.
-
-  When used in a `JaxprEqn`, `input_index` refers to `eqn.invars`.
-  When used in a `Jaxpr`, `input_index` refers to `jaxpr.constvars + jaxpr.invars`.
   """
 
-  def __init__(self, input_index: Any):
-    self.input_index = input_index
-
-  def replace(self, *, input_index: Any | None = None):
-    if input_index is None:
-      input_index = self.input_index
-    return self.__class__(input_index)
-
   def __eq__(self, other):
     if not isinstance(other, JaxprInputEffect):
       return NotImplemented
-    return self.input_index == other.input_index
+    return True
 
   def __hash__(self):
-    return hash((self.__class__, self.input_index))
+    return hash(self.__class__)
 
   def __repr__(self):
-    return f"{self.__class__.__name__}({self.input_index})"
+    return f"{self.__class__.__name__}()"
 
 class EffectTypeSet:
 
diff --git a/jax/_src/interpreters/ad.py b/jax/_src/interpreters/ad.py
index 7e5aacba3d80..9a731f3449ba 100644
--- a/jax/_src/interpreters/ad.py
+++ b/jax/_src/interpreters/ad.py
@@ -1473,11 +1473,8 @@ def rearrange_binders(jaxpr: core.ClosedJaxpr, primals_in, tangents_in, primals_
   new_debug_info = jaxpr.jaxpr.debug_info._replace(
       arg_names=new_arg_names, result_paths=new_result_paths)
   constvars = jaxpr.jaxpr.constvars
-  new_effects = pe._renumber_effects(
-      (*constvars, *new_invars), (*constvars, *jaxpr.jaxpr.invars),
-      jaxpr.jaxpr.effects)
   new_jaxpr = core.Jaxpr(constvars, new_invars, new_outvars, jaxpr.jaxpr.eqns,
-                         new_effects, new_debug_info)
+                         jaxpr.jaxpr.effects, new_debug_info)
   return core.ClosedJaxpr(new_jaxpr, jaxpr.consts)
 
 def _perm(primal_counts: Sequence[int], tangent_counts: Sequence[int],
diff --git a/jax/_src/interpreters/partial_eval.py b/jax/_src/interpreters/partial_eval.py
index 0101c45a3331..5c6c1515e820 100644
--- a/jax/_src/interpreters/partial_eval.py
+++ b/jax/_src/interpreters/partial_eval.py
@@ -1601,11 +1601,7 @@ def _move_invars_right(jaxpr: ClosedJaxpr, to_move: tuple[bool, ...]):
   invars, rest = split_list(jaxpr.jaxpr.invars, [len(to_move)])
   left_invars, right_invars = partition_list(to_move, invars)
   new_invars = [*left_invars, *right_invars, *rest]
-  new_effs = _renumber_effects(
-      (*jaxpr.jaxpr.constvars, *new_invars),
-      (*jaxpr.jaxpr.constvars, *jaxpr.jaxpr.invars),
-      jaxpr.jaxpr.effects)
-  new_jaxpr = jaxpr.jaxpr.replace(invars=new_invars, effects=new_effs)
+  new_jaxpr = jaxpr.jaxpr.replace(invars=new_invars)
   return jaxpr.replace(jaxpr=new_jaxpr)
 
 def move_binders_to_front(closed_jaxpr: ClosedJaxpr, to_move: Sequence[bool]
@@ -1619,23 +1615,15 @@ def _move_binders_to_front(jaxpr: ClosedJaxpr, to_move: tuple[bool, ...]
   assert len(jaxpr.in_avals) == len(to_move)
   constvars, invars = jaxpr.jaxpr.constvars, jaxpr.jaxpr.invars
   new_invars = _move_to_front(invars, to_move)
-  new_effs = _renumber_effects(
-      (*constvars, *new_invars), (*constvars, *invars), jaxpr.jaxpr.effects)
   if jaxpr.jaxpr.debug_info.arg_names is None:
     new_arg_names = None
   else:
     new_arg_names = tuple(_move_to_front(jaxpr.jaxpr.debug_info.arg_names, to_move))
   dbg = jaxpr.jaxpr.debug_info._replace(arg_names=new_arg_names)
   new_jaxpr = jaxpr.jaxpr.replace(
-      constvars=constvars, invars=new_invars, effects=new_effs, debug_info=dbg)
+      constvars=constvars, invars=new_invars, debug_info=dbg)
   return core.ClosedJaxpr(new_jaxpr, jaxpr.consts)
 
-def _renumber_effects(new_vars, old_vars, effs):
-  newvar_idxs = {id(v): i for i, v in enumerate(new_vars)}
-  old_to_new = {i: newvar_idxs[id(v)] for i, v in enumerate(old_vars)}
-  return {e.replace(input_index=old_to_new[e.input_index])
-          if isinstance(e, effects.JaxprInputEffect) else e for e in effs}
-
 def _move_to_front(lst: Sequence, to_move: Sequence[bool]) -> Sequence:
   return ([elt for elt, move in zip(lst, to_move) if move] +
           [elt for elt, move in zip(lst, to_move) if not move])
@@ -1763,35 +1751,6 @@ def make_jaxpr_effects(constvars, invars, outvars, eqns) -> effects.Effects:
       all_vars[outvar] = None  # type: ignore
       mut_arrays.add(outvar)
     for eff in eqn.effects:
-      if isinstance(eff, effects.JaxprInputEffect):
-        if eff.input_index >= len(eqn.invars):
-          # TODO(mattjj): ask for forgiveness
-          dbg = type('Fake', (), {'resolve_result_paths': lambda self_: self_,
-                                  'assert_arg_names': lambda _, __: None,
-                                  'assert_result_paths': lambda _, __: None,
-                                  })()
-          raise ValueError(
-              f"`JaxprInputEffect` {eff} is invalid."
-              f"\n Equation: {eqn}\n"
-              "\n Jaxpr: "
-              f"{core.Jaxpr(constvars, invars, outvars, eqns, set(), dbg)}")  # type: ignore
-        eqn_invar = eqn.invars[eff.input_index]
-        if type(eqn_invar) is core.Literal or eqn_invar in mut_arrays:
-          continue
-        if (input_index := all_vars.get(eqn_invar, sentinel)) is sentinel:
-          # TODO(mattjj): ask for forgiveness
-          dbg = type('Fake', (), {'resolve_result_paths': lambda self_: self_,
-                                  'assert_arg_names': lambda _, __: None,
-                                  'assert_result_paths': lambda _, __: None,
-                                  })()
-          raise ValueError(
-                f"`JaxprInputEffect` {eff} does not have "
-                f"corresponding jaxpr input: {eqn_invar=}."
-                f"\n Equation: {eqn}\n"
-                f"\n Effects: {eqn.effects}\n"
-                "\n Jaxpr: "
-                f"{core.Jaxpr(constvars, invars, outvars, eqns, set(), dbg)}")  # type: ignore
-        eff = eff.replace(input_index=input_index)
       jaxpr_effects.add(eff)
   return jaxpr_effects
 
diff --git a/jax/_src/lax/control_flow/common.py b/jax/_src/lax/control_flow/common.py
index 173297e4d8a1..99d8a398efd0 100644
--- a/jax/_src/lax/control_flow/common.py
+++ b/jax/_src/lax/control_flow/common.py
@@ -96,9 +96,7 @@ def _pad_constvars(jaxpr: core.Jaxpr, left: tuple[core.AvalQDD, ...],
   def make_var(aq):
     return core.Var(aq.aval, initial_qdd=aq.qdd, final_qdd=aq.qdd)
   constvars = [*map(make_var, left), *jaxpr.constvars, *map(make_var, right)]
-  effs = pe._renumber_effects([*constvars, *jaxpr.invars],
-                              [*jaxpr.constvars, *jaxpr.invars], jaxpr.effects)
-  jaxpr = jaxpr.replace(constvars=constvars, effects=effs)
+  jaxpr = jaxpr.replace(constvars=constvars)
   config.enable_checks.value and core.check_jaxpr(jaxpr)
   return jaxpr
 
@@ -112,11 +110,7 @@ def _dedup_consts(jaxpr, const_ids):
   outvars = [canonicalize.get(x, x) if isinstance(x, core.Var) else x
              for x in jaxpr.outvars]
   constvars = list(newvars.values())
-  effs = pe._renumber_effects(
-      [*constvars, *jaxpr.invars],
-      [*map(canonicalize.get, jaxpr.constvars), *jaxpr.invars], jaxpr.effects)
-  jaxpr = jaxpr.replace(constvars=constvars, eqns=eqns, outvars=outvars,
-                        effects=effs)
+  jaxpr = jaxpr.replace(constvars=constvars, eqns=eqns, outvars=outvars)
   config.enable_checks.value and core.check_jaxpr(jaxpr)
   return jaxpr
 
diff --git a/jax/_src/lax/control_flow/conditionals.py b/jax/_src/lax/control_flow/conditionals.py
index 808545622608..0b9dfdce2d54 100644
--- a/jax/_src/lax/control_flow/conditionals.py
+++ b/jax/_src/lax/control_flow/conditionals.py
@@ -445,9 +445,6 @@ def _join_cond_effects(branches: Sequence[core.ClosedJaxpr]) -> effects.Effects:
   joined_effects = set()
   for b in branches:
     for eff in b.effects:
-      if isinstance(eff, effects.JaxprInputEffect):
-        # Offset index to handle predicate
-        eff = eff.replace(input_index=eff.input_index + 1)
       joined_effects.add(eff)
   return joined_effects
 
diff --git a/jax/_src/lax/control_flow/loops.py b/jax/_src/lax/control_flow/loops.py
index 84a6b2d0bbfe..69a5781488c8 100644
--- a/jax/_src/lax/control_flow/loops.py
+++ b/jax/_src/lax/control_flow/loops.py
@@ -919,13 +919,7 @@ def _rearrange_mutable_binders(
     immut_names, mut_names = partition_list(is_mutable, names)
     new_arg_names = [*fst, *mut_names, *immut_names, *rst]
   dbg = jaxpr.jaxpr.debug_info._replace(arg_names=new_arg_names)
-
-  # TODO(mattjj): don't we need to re-number effects? test coverage?
-  new_effs = pe._renumber_effects((*jaxpr.jaxpr.constvars, *new_invars),
-                                  (*jaxpr.jaxpr.constvars, *jaxpr.jaxpr.invars),
-                                  jaxpr.jaxpr.effects)
-  new_jaxpr = jaxpr.jaxpr.replace(invars=new_invars, effects=new_effs,
-                                  debug_info=dbg)
+  new_jaxpr = jaxpr.jaxpr.replace(invars=new_invars, debug_info=dbg)
   if config.enable_checks.value: core.check_jaxpr(new_jaxpr)
   return ClosedJaxpr(new_jaxpr, jaxpr.consts)
 
@@ -1777,16 +1771,8 @@ def _join_while_effects(body_jaxpr, cond_jaxpr, body_nconsts, cond_nconsts
                        ) -> effects.Effects:
   joined_effects = set()
   for eff in cond_jaxpr.effects:
-    if isinstance(eff, effects.JaxprInputEffect):
-      index = eff.input_index
-      if index >= cond_nconsts:
-        index += body_nconsts
-      eff = eff.replace(input_index=index)
     joined_effects.add(eff)
   for eff in body_jaxpr.effects:
-    if isinstance(eff, effects.JaxprInputEffect):
-      index = eff.input_index + cond_nconsts
-      eff = eff.replace(input_index=index)
     joined_effects.add(eff)
   return joined_effects
 
@@ -2285,17 +2271,6 @@ def _while_partial_discharge_rule(should_discharge, in_avals, out_avals, *args,
                                                                  [cond_nconsts,
                                                                   body_nconsts])
 
-  # Check if the same Ref is written to in both cond and body.
-  cond_write_ids = {id(cond_consts_avals[effect.input_index])
-    for effect in cond_jaxpr.effects if isinstance(effect, state.WriteEffect)}
-  cond_has_writes = len(cond_write_ids) > 0
-  body_write_ids = {id(body_consts_avals[effect.input_index])
-    for effect in body_jaxpr.effects if isinstance(effect, state.WriteEffect)}
-  write_to_both_ids = cond_write_ids & body_write_ids
-  if write_to_both_ids:
-    raise NotImplementedError(
-        "Cannot write to the same ref in both cond and body of while loop.")
-
   cond_is_ref = [
       isinstance(aval, state.AbstractRef) and should
       for aval, should in zip(cond_consts_avals, cond_consts_discharge)
@@ -2315,13 +2290,6 @@ def _while_partial_discharge_rule(should_discharge, in_avals, out_avals, *args,
   num_body_refs = sum(body_is_ref)
   num_remaining_body_consts = body_nconsts - num_body_refs
   num_out_body_consts = num_remaining_body_consts
-  if cond_has_writes:
-    # If the cond has writes, we need to add the cond consts into the body
-    # consts since we need to evaluate the cond condition in the body.
-    remaining_body_consts = [*remaining_cond_consts, *remaining_body_consts]
-    remaining_body_const_avals = [*remaining_cond_const_avals,
-                                  *remaining_body_const_avals]
-    num_remaining_body_consts += num_remaining_cond_consts
 
   num_carry = len(in_avals) - body_nconsts - cond_nconsts
   body_jaxpr, body_jaxpr_consts = body_jaxpr.jaxpr, body_jaxpr.consts
@@ -2353,23 +2321,8 @@ def new_body(*consts_refs_carry):
     consts, body_refs, cond_refs, carry = split_list(
         consts_refs_carry,
         [num_remaining_body_consts, num_body_refs, num_cond_refs])
-    if cond_has_writes:
-      # We run the cond jaxpr in the body so that Refs that are updated
-      # in the cond jaxpr are persisted via the carry.
-      cond_consts, body_consts = split_list(consts, [num_remaining_cond_consts])
-      cond_consts_and_refs = merge_lists(cond_is_ref, cond_consts, cond_refs)
-      cond_carry_refs = core.eval_jaxpr(discharged_cond_jaxpr, (),
-                                  *cond_consts_and_refs,
-                                  *carry)
-      # Note: in order to handle the same Ref being updated in both the cond
-      # and body, we would need to interleave the updated cond_carry_refs into
-      # body_refs here.
-      # Currently we disallow this so we don't need to handle it.
-      _, cond_refs_out = split_list(cond_carry_refs, [1])
-      assert len(cond_refs_out) == len(cond_refs)
-    else:
-      body_consts = consts
-      cond_refs_out = cond_refs
+    body_consts = consts
+    cond_refs_out = cond_refs
 
     body_consts_and_refs = merge_lists(body_is_ref, body_consts, body_refs)
     body_carry_refs = core.eval_jaxpr(discharged_body_jaxpr, (),
diff --git a/jax/_src/pjit.py b/jax/_src/pjit.py
index 62b00483fb1e..79e60593deac 100644
--- a/jax/_src/pjit.py
+++ b/jax/_src/pjit.py
@@ -1833,18 +1833,9 @@ def _pjit_typecheck(ctx_factory, *in_atoms, jaxpr, **params):
 
 
 def _pjit_abstract_eval(*args, jaxpr, out_shardings, **_):
-  effs = _pjit_eqn_effects(jaxpr) if jaxpr.constvars else jaxpr.effects
-  return jaxpr.out_avals, effs
+  return jaxpr.out_avals, jaxpr.effects
 jit_p.def_effectful_abstract_eval(_pjit_abstract_eval)
 
-def _pjit_eqn_effects(jaxpr):
-  # jaxpr input effects are indexed to include jaxpr.constvars, but the pjit eqn
-  # should have effects indexed only on its explicit arguments
-  effs = jaxpr.effects
-  return {e.replace(input_index=e.input_index - len(jaxpr.constvars))
-          if isinstance(e, effects.JaxprInputEffect) else e for e in effs}
-
-
 def _pjit_cached_lower_jaxpr_to_fun(ctx: mlir.LoweringRuleContext,
                                     name: str, jaxpr: core.ClosedJaxpr,
                                     num_const_args: int, in_avals,
@@ -2512,7 +2503,7 @@ def keep_where(xs, keeps):
   if not any(used_inputs) and not any(used_outputs) and not dced_jaxpr.effects:
     return used_inputs, None
   else:
-    new_effs = _pjit_eqn_effects(dced_jaxpr)
+    new_effs = dced_jaxpr.effects
     new_eqn = core.new_jaxpr_eqn(
         [v for v, used in zip(eqn.invars, used_inputs) if used],
         [v for v, used in zip(eqn.outvars, used_outputs) if used],
diff --git a/jax/_src/state/__init__.py b/jax/_src/state/__init__.py
index adf7926d7dbd..7cc4260a8b11 100644
--- a/jax/_src/state/__init__.py
+++ b/jax/_src/state/__init__.py
@@ -21,7 +21,6 @@
     Transform as Transform,
     TransformedRef as TransformedRef,
     WriteEffect as WriteEffect,
-    get_ref_state_effects as get_ref_state_effects,
     get_transforms_shape as get_transforms_shape,
     shaped_array_ref as shaped_array_ref,
 )
diff --git a/jax/_src/state/discharge.py b/jax/_src/state/discharge.py
index a20d5648217b..17bf7a47408f 100644
--- a/jax/_src/state/discharge.py
+++ b/jax/_src/state/discharge.py
@@ -685,39 +685,10 @@ def _run_state_abstract_eval(*avals: core.AbstractValue, jaxpr: core.Jaxpr,
                              is_initialized: tuple[bool, ...]):
   del which_linear
   assert sum(is_initialized) == len(avals)
-  # When we abstractly evaluate `run_state`, we want to keep track of which
-  # input avals are `Ref`s and which are not. If an aval is a `Ref`, we want to
-  # "propagate" out its inner effects. Otherwise, the effects are local to this
-  # `run_state`.
-  inner_to_outer_aval_mapping = {}
-  outer_ref_index = 0
-  for i, is_init in enumerate(is_initialized):
-    if not is_init:
-      pass
-    inner_to_outer_aval_mapping[i] = outer_ref_index
-    outer_ref_index += 1
-  nonlocal_effects = set()
-  is_ref = {i for i, aval in enumerate(avals) if isinstance(aval, AbstractRef)}
-  for eff in jaxpr.effects:
-    if not isinstance(eff, RefEffect):
-      nonlocal_effects.add(eff)
-      continue
-    if eff.input_index not in inner_to_outer_aval_mapping:
-      # This means that this effect corresponds to an uninitialized Ref and
-      # should not propagate out of the primitive.
-      continue
-    # If we do propagate the effect, we need to update the input index to
-    # correspond to the outer index.
-    outer_index = inner_to_outer_aval_mapping[eff.input_index]
-    if outer_index in is_ref:
-      # This means that the effect corresponds to a Ref from an outside scope.
-      nonlocal_effects.add(
-          eff.replace(input_index=inner_to_outer_aval_mapping[eff.input_index])
-      )
   assert len(jaxpr.invars) == len(is_initialized)
   if not all(is_initialized):
     raise NotImplementedError  # Uninitialized refs are not in avals.
-  return avals, nonlocal_effects
+  return avals, jaxpr.effects
 run_state_p.def_effectful_abstract_eval(_run_state_abstract_eval)
 
 def _run_state_jvp(primals: Sequence[Any], tangents: Sequence[Any], *,
diff --git a/jax/_src/state/primitives.py b/jax/_src/state/primitives.py
index 493ddc962b3b..dfca0f3cc01d 100644
--- a/jax/_src/state/primitives.py
+++ b/jax/_src/state/primitives.py
@@ -434,7 +434,7 @@ def _get_abstract_eval(ref_aval: AbstractRef, *args,
     if transforms:
       raise ValueError("Cannot index non-shaped array with nontrivial indices.")
     out_aval = ref_aval.inner_aval
-  return (out_aval, {ReadEffect(0)})
+  return (out_aval, {ReadEffect()})
 get_p.def_effectful_abstract_eval(_get_abstract_eval)
 
 def _swap_abstract_eval(ref_aval: AbstractRef,
@@ -471,7 +471,7 @@ def _swap_abstract_eval(ref_aval: AbstractRef,
     if transforms:
       raise ValueError("Cannot index non-shaped array with nontrivial indices.")
     out_aval = ref_aval.inner_aval
-  return (out_aval, {WriteEffect(0)})
+  return (out_aval, {WriteEffect()})
 swap_p.def_effectful_abstract_eval(_swap_abstract_eval)
 
 
@@ -508,7 +508,7 @@ def _addupdate_abstract_eval(ref_aval: AbstractRef,
     # Check that the transforms are valid
     if transforms:
       raise ValueError("Cannot index non-shaped array with nontrivial indices.")
-  return [], {AccumEffect(0)}
+  return [], {AccumEffect()}
 addupdate_p.def_effectful_abstract_eval(_addupdate_abstract_eval)
 
 ## Pretty printing for `get` and `swap` in jaxprs
diff --git a/jax/_src/state/types.py b/jax/_src/state/types.py
index 2644f8392416..8332db347b6d 100644
--- a/jax/_src/state/types.py
+++ b/jax/_src/state/types.py
@@ -45,12 +45,10 @@ class RefEffect(effects.JaxprInputEffect):
   name: str
 
   def __eq__(self, other):
-    if not isinstance(other, self.__class__):
-      return False
-    return self.input_index == other.input_index
+    return isinstance(other, self.__class__)
 
   def __hash__(self):
-    return hash((self.__class__, self.input_index))
+    return hash(self.__class__)
 
   def _pretty_print(self, context: core.JaxprPpContext) -> pp.Doc:
     if isinstance(self.input_index, core.Var):
@@ -572,13 +570,6 @@ def _unmap_ref(size, axis, explicit_mesh_axis, ref_aval):
 
 core.aval_mapping_handlers[AbstractRef] = (_map_ref, _unmap_ref)
 
-def get_ref_state_effects(
-    avals: Sequence[core.AbstractValue],
-    effects: core.Effects) -> list[set[StateEffect]]:
-  return [{eff for eff in effects
-           if isinstance(eff, (ReadEffect, WriteEffect, AccumEffect))
-           and eff.input_index == i} for i, _ in enumerate(avals)]
-
 def shaped_array_ref(
     shape: tuple[int, ...], dtype, weak_type: bool = False) -> AbstractRef:
   return AbstractRef(core.ShapedArray(shape, dtype, weak_type=weak_type))
diff --git a/tests/state_test.py b/tests/state_test.py
index 8441abb21e73..b6a66a65ed43 100644
--- a/tests/state_test.py
+++ b/tests/state_test.py
@@ -128,8 +128,7 @@ def f(x_ref):
     else:
       jaxpr, out_avals, _ = pe.trace_to_jaxpr_dynamic(
           wrap_init(f, 1), [ref_aval])
-      self.assertSetEqual(jaxpr.effects,
-                          {ReadEffect(len(jaxpr.constvars))})
+      self.assertSetEqual(jaxpr.effects, {ReadEffect()})
       self.assertLen(out_avals, 1)
       out_aval, = out_avals
       self.assertIsInstance(out_aval, core.ShapedArray)
@@ -225,8 +224,7 @@ def f(x_ref, val):
     else:
       jaxpr, out_avals, _ = pe.trace_to_jaxpr_dynamic(
           wrap_init(f, 2), [ref_aval, val_aval])
-      self.assertSetEqual(jaxpr.effects,
-                          {WriteEffect(len(jaxpr.constvars))})
+      self.assertSetEqual(jaxpr.effects, {WriteEffect()})
       self.assertLen(out_avals, 1)
       out_aval, = out_avals
       self.assertIsInstance(out_aval, core.ShapedArray)
@@ -302,8 +300,7 @@ def f(x_ref, val):
     else:
       jaxpr, out_avals, _ = pe.trace_to_jaxpr_dynamic(
           wrap_init(f, 2), [ref_aval, val_aval])
-      self.assertSetEqual(jaxpr.effects,
-                          {AccumEffect(len(jaxpr.constvars))})
+      self.assertSetEqual(jaxpr.effects, {AccumEffect()})
       self.assertLen(out_avals, 0)
 
   def test_addupdate_abstract_eval_must_take_in_refs(self):
@@ -738,8 +735,7 @@ def f(a_ref, b_ref):
     self.assertLen(discharged_jaxpr.outvars, 1)
     self.assertIsInstance(discharged_jaxpr.invars[0].aval, AbstractRef)
     self.assertIsInstance(discharged_jaxpr.invars[1].aval, core.ShapedArray)
-    self.assertEqual(discharged_jaxpr.effects,
-        {WriteEffect(len(discharged_jaxpr.constvars))})
+    self.assertEqual(discharged_jaxpr.effects, {WriteEffect()})
 
   def test_ellipsis_index(self):
     def f(ref):
@@ -781,8 +777,8 @@ def body(i, st):
     f_jaxpr = jax.make_jaxpr(f)(ref(1.), ref(2.))
     jaxpr, _ = discharge_state(f_jaxpr.jaxpr, (), should_discharge=[False, True])
     # Effects on y_ref were discharged away but not the effects on x_ref
-    self.assertEqual(f_jaxpr.effects, {ReadEffect(0), WriteEffect(0), ReadEffect(1), WriteEffect(1)})
-    self.assertEqual(jaxpr.effects, {ReadEffect(0), WriteEffect(0)})
+    self.assertEqual(f_jaxpr.effects, {ReadEffect(), WriteEffect(), ReadEffect(), WriteEffect()})
+    self.assertEqual(jaxpr.effects, {ReadEffect(), WriteEffect()})
     # x_ref arg is still a reference but y_ref is discharged
     self.assertNotIsInstance(jaxpr.invars[1].aval, AbstractRef)
     self.assertIsInstance(jaxpr.invars[0].aval, AbstractRef)
@@ -1104,8 +1100,8 @@ def false_fun():
     f_jaxpr = jax.make_jaxpr(f0)(False, ref(3.), ref(4.))
     jaxpr, _ = discharge_state(f_jaxpr.jaxpr, (), should_discharge=[False, False, True])
     # Effects on y_ref were discharged away but not the effects on x_ref
-    self.assertEqual(f_jaxpr.effects, {ReadEffect(1), WriteEffect(1), ReadEffect(2), WriteEffect(2)})
-    self.assertEqual(jaxpr.effects, {ReadEffect(1), WriteEffect(1)})
+    self.assertEqual(f_jaxpr.effects, {ReadEffect(), WriteEffect(), ReadEffect(), WriteEffect()})
+    self.assertEqual(jaxpr.effects, {ReadEffect(), WriteEffect()})
     # x_ref arg is still a reference but y_ref is discharged
     self.assertNotIsInstance(jaxpr.invars[2].aval, AbstractRef)
     self.assertIsInstance(jaxpr.invars[1].aval, AbstractRef)
@@ -1493,10 +1489,10 @@ def inner(y_ref):
     self.assertEmpty(jaxpr.effects)
     self.assertEmpty(jaxpr.jaxpr.eqns[0].effects)
     self.assertSetEqual(jaxpr.jaxpr.eqns[0].params["jaxpr"].effects,
-                        {ReadEffect(0)})
+                        {ReadEffect()})
     self.assertSetEqual(
         jaxpr.jaxpr.eqns[0].params["jaxpr"].eqns[0].params["jaxpr"].effects,
-                        {ReadEffect(0), ReadEffect(1)})
+                        {ReadEffect(), ReadEffect()})
 
   def test_jvp_of_run_state(self):
     @run_state