diff --git a/jax/_src/pjit.py b/jax/_src/pjit.py
index 16d301b74abd..a59c0cdeeeb3 100644
--- a/jax/_src/pjit.py
+++ b/jax/_src/pjit.py
@@ -1813,17 +1813,17 @@ def _pjit_typecheck(ctx_factory, *in_atoms, jaxpr, **params):
 
 
 def _pjit_abstract_eval(*args, jaxpr, out_shardings, **_):
-  # jaxpr input effects are indexed to include jaxpr.constvars, but the pjit eqn
-  # should have effects indexed only on its explicit arguments
-  if jaxpr.constvars:
-    effs = {e.replace(input_index=e.input_index - len(jaxpr.constvars))
-            if isinstance(e, effects.JaxprInputEffect)
-            else e for e in jaxpr.effects}
-  else:
-    effs = jaxpr.effects
+  effs = _pjit_eqn_effects(jaxpr) if jaxpr.constvars else jaxpr.effects
   return jaxpr.out_avals, effs
 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,
@@ -2491,10 +2491,11 @@ 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_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],
-        eqn.primitive, new_params, dced_jaxpr.effects, eqn.source_info, eqn.ctx)
+        eqn.primitive, new_params, new_effs, eqn.source_info, eqn.ctx)
     return used_inputs, new_eqn
 
 pe.dce_rules[jit_p] = dce_jaxpr_pjit_rule
diff --git a/tests/jaxpr_effects_test.py b/tests/jaxpr_effects_test.py
index 997ba86c16bd..67120364ee28 100644
--- a/tests/jaxpr_effects_test.py
+++ b/tests/jaxpr_effects_test.py
@@ -276,6 +276,42 @@ def foo(w):
 
     foo(jax.new_ref(jnp.eye(1)))  # don't crash
 
+  def test_cond_const_input_effect_indexing(self):
+    @jax.custom_jvp
+    def weird(x):
+      return x
+
+    @weird.defjvp
+    def weird_jvp(primals, tangents):
+      (x,), (xdot,) = primals, tangents
+      return jnp.sum(np.ones(3)) * x, xdot
+
+    @jax.jit
+    def f(x):
+      x_ref = jax.new_ref(0.)
+      return jax.lax.cond(x < 0, lambda: x_ref[...], lambda: weird(x[...]))
+
+    jax.jvp(f, (1.,), (1.,))
+
+  def test_scan_const_input_effect_indexing(self):
+    @jax.custom_jvp
+    def weird(x):
+      return x
+
+    @weird.defjvp
+    def weird_jvp(primals, tangents):
+      (x,), (xdot,) = primals, tangents
+      return jnp.sum(np.ones(3)) * x, xdot
+
+    @jax.jit
+    def f(x):
+      x_ref = jax.new_ref(0.)
+      y, () = jax.lax.scan(lambda _, __: (weird(x_ref[...]), ()),
+                           x_ref[...], length=1)
+      return y
+
+    jax.jvp(f, (1.,), (1.,))
+
 
 @jtu.thread_unsafe_test_class()  # because of mlir.register_lowering calls
 class EffectfulJaxprLoweringTest(jtu.JaxTestCase):