diff --git a/jax/interpreters/partial_eval.py b/jax/interpreters/partial_eval.py
index 9d9bdee1033b..0ee787810499 100644
--- a/jax/interpreters/partial_eval.py
+++ b/jax/interpreters/partial_eval.py
@@ -1215,20 +1215,31 @@ def find_progenitors(self, tracer):
 def _prune_convert_element_types(jaxpr, constvals):
   consts = dict(zip(jaxpr.constvars, constvals))
   new_eqns = []
+  var_subs: Dict[Var, Var] = {}
   for eqn in jaxpr.eqns:
+    # apply invar substitutions
+    eqn = JaxprEqn([var_subs.get(v, v) for v in eqn.invars], eqn.outvars,
+                   eqn.primitive, eqn.params, eqn.source_info)
     if eqn.primitive is core.convert_element_type_p:
       c = consts.get(eqn.invars[0])
       if type(c) in core.literalable_types and not np.shape(c):
         # constant-fold dtype conversion of literals to be inlined
         consts[eqn.outvars[0]] = np.array(c, eqn.params['new_dtype'])
         continue
-      if c is not None and dtypes.dtype(c) == eqn.params['new_dtype']:
-        # don't stage out no-op convert_element_type calls as clutter
+      elif c is not None and dtypes.dtype(c) == eqn.params['new_dtype']:
+        # don't include no-op convert_element_type calls on consts; instead,
+        # just make the outvar refer to the constant, and skip the eqn
         consts[eqn.outvars[0]] = c
         continue
+      elif c is None and eqn.invars[0].aval.dtype == eqn.params['new_dtype']:
+        # don't include no-op convert_element_type calls on vars; instead,
+        # substitute all occurences of the outvar with the invar, and skip eqn
+        var_subs[eqn.outvars[0]] = eqn.invars[0]
+        continue
     new_eqns.append(eqn)
   new_constvars, new_constvals = unzip2(consts.items())
-  new_jaxpr = Jaxpr(new_constvars, jaxpr.invars, jaxpr.outvars, new_eqns)
+  new_outvars = [var_subs.get(v, v) for v in jaxpr.outvars]
+  new_jaxpr = Jaxpr(new_constvars, jaxpr.invars, new_outvars, new_eqns)
   return new_jaxpr, new_constvals
 
 def _inline_literals(jaxpr, constvals):
diff --git a/tests/api_test.py b/tests/api_test.py
index 5aecec55d3b9..994c5bfa1f2a 100644
--- a/tests/api_test.py
+++ b/tests/api_test.py
@@ -3176,6 +3176,19 @@ def test_jnp_array_doesnt_device_put(self):
       api.make_jaxpr(lambda: jnp.array(3))()
     self.assertEqual(count[0], 0)
 
+  def test_elide_trivial_convert_element_types(self):
+    if config.x64_enabled:
+      x = jnp.float64(1.)
+    else:
+      x = jnp.float32(1.)
+
+    jaxpr = api.make_jaxpr(lambda x, y: x + y)(x, 2.)
+    self.assertLen(jaxpr.eqns, 1)
+
+    cet = partial(lax.convert_element_type, new_dtype=x.dtype)
+    jaxpr = api.make_jaxpr(lambda x: cet(cet(cet(x))))(1.)
+    self.assertLen(jaxpr.eqns, 0)
+
 
 class RematTest(jtu.JaxTestCase):