diff --git a/pymc/distributions/continuous.py b/pymc/distributions/continuous.py
index 7a0d044cc..d5e69fc79 100644
--- a/pymc/distributions/continuous.py
+++ b/pymc/distributions/continuous.py
@@ -1373,13 +1373,12 @@ class Exponential(PositiveContinuous):
     rv_op = exponential
 
     @classmethod
-    def dist(cls, lam=None, scale=None, *args, **kwargs):
-        if lam is not None and scale is not None:
+    def dist(cls, lam=None, *, scale=None, **kwargs):
+        if lam is None and scale is None:
+            scale = 1.0
+        elif lam is not None and scale is not None:
             raise ValueError("Incompatible parametrization. Can't specify both lam and scale.")
-        elif lam is None and scale is None:
-            raise ValueError("Incompatible parametrization. Must specify either lam or scale.")
-
-        if scale is None:
+        elif lam is not None:
             scale = pt.reciprocal(lam)
 
         scale = pt.as_tensor_variable(scale)
diff --git a/pymc/step_methods/hmc/nuts.py b/pymc/step_methods/hmc/nuts.py
index cc29e0334..770605f4b 100644
--- a/pymc/step_methods/hmc/nuts.py
+++ b/pymc/step_methods/hmc/nuts.py
@@ -242,24 +242,24 @@ def competence(var, has_grad):
 
 class _Tree:
     __slots__ = (
-        "ndim",
-        "integrator",
-        "start",
-        "step_size",
         "Emax",
-        "start_energy",
-        "rng",
-        "left",
-        "right",
-        "proposal",
         "depth",
-        "log_size",
+        "floatX",
+        "integrator",
+        "left",
         "log_accept_sum",
+        "log_size",
+        "max_energy_change",
         "mean_tree_accept",
         "n_proposals",
+        "ndim",
         "p_sum",
-        "max_energy_change",
-        "floatX",
+        "proposal",
+        "right",
+        "rng",
+        "start",
+        "start_energy",
+        "step_size",
     )
 
     def __init__(
diff --git a/tests/distributions/test_continuous.py b/tests/distributions/test_continuous.py
index 41504816a..2864335e3 100644
--- a/tests/distributions/test_continuous.py
+++ b/tests/distributions/test_continuous.py
@@ -461,15 +461,6 @@ def test_exponential(self):
             lambda q, lam: st.expon.ppf(q, loc=0, scale=1 / lam),
         )
 
-    def test_exponential_wrong_arguments(self):
-        msg = "Incompatible parametrization. Can't specify both lam and scale"
-        with pytest.raises(ValueError, match=msg):
-            pm.Exponential.dist(lam=0.5, scale=5)
-
-        msg = "Incompatible parametrization. Must specify either lam or scale"
-        with pytest.raises(ValueError, match=msg):
-            pm.Exponential.dist()
-
     def test_laplace(self):
         check_logp(
             pm.Laplace,
@@ -2274,8 +2265,20 @@ class TestExponential(BaseTestDistributionRandom):
     checks_to_run = [
         "check_pymc_params_match_rv_op",
         "check_pymc_draws_match_reference",
+        "check_both_lam_scale_raises",
+        "check_default_scale",
     ]
 
+    def check_both_lam_scale_raises(self):
+        msg = "Incompatible parametrization. Can't specify both lam and scale"
+        with pytest.raises(ValueError, match=msg):
+            pm.Exponential.dist(lam=0.5, scale=5)
+
+    def check_default_scale(self):
+        rv = self.pymc_dist.dist()
+        [scale] = rv.owner.op.dist_params(rv.owner)
+        assert scale.data == 1.0
+
 
 class TestExponentialScale(BaseTestDistributionRandom):
     pymc_dist = pm.Exponential