diff --git a/python/mujoco/bindings_test.py b/python/mujoco/bindings_test.py
index 9f1f61d0..c4544d7a 100644
--- a/python/mujoco/bindings_test.py
+++ b/python/mujoco/bindings_test.py
@@ -737,6 +737,7 @@ Euler integrator, semi-implicit in velocity.
 
   def test_float_constant(self):
     self.assertEqual(mujoco.mjMAXVAL, 1e10)
+    self.assertEqual(mujoco.mjMINVAL, 1e-15)
 
   def test_string_constants(self):
     self.assertLen(mujoco.mjDISABLESTRING, mujoco.mjtDisableBit.mjNDISABLE)
diff --git a/python/mujoco/constants.cc b/python/mujoco/constants.cc
index 2ffe73bb..b8327c75 100644
--- a/python/mujoco/constants.cc
+++ b/python/mujoco/constants.cc
@@ -78,6 +78,9 @@ PYBIND11_MODULE(_constants, pymodule) {
   // from mujoco.h
   X(mjVERSION_HEADER);
 
+  // from mjtnum.h
+  X(mjMINVAL);
+
   #undef X
   pymodule.attr("mjDISABLESTRING") = MakeTuple(mjDISABLESTRING);
   pymodule.attr("mjENABLESTRING") = MakeTuple(mjENABLESTRING);
diff --git a/python/mujoco/viewer.py b/python/mujoco/viewer.py
index 0d0aa942..0c6d7c3b 100644
--- a/python/mujoco/viewer.py
+++ b/python/mujoco/viewer.py
@@ -136,7 +136,8 @@ def _physics_loop(simulate: Simulate, loader: Optional[_InternalLoaderType]):
           # Inject noise.
           if simulate.ctrlnoisestd != 0.0:
             # Convert rate and scale to discrete time (Ornstein–Uhlenbeck).
-            rate = math.exp(-m.opt.timestep / simulate.ctrlnoiserate)
+            rate = math.exp(-m.opt.timestep /
+                            max(simulate.ctrlnoiserate, mujoco.mjMINVAL))
             scale = simulate.ctrlnoisestd * math.sqrt(1 - rate * rate)
 
             for i in range(m.nu):
diff --git a/simulate/main.cc b/simulate/main.cc
index 704b38f5..d26481e4 100644
--- a/simulate/main.cc
+++ b/simulate/main.cc
@@ -330,7 +330,7 @@ void PhysicsLoop(mj::Simulate& sim) {
           // inject noise
           if (sim.ctrlnoisestd) {
             // convert rate and scale to discrete time (Ornstein–Uhlenbeck)
-            mjtNum rate = mju_exp(-m->opt.timestep / sim.ctrlnoiserate);
+            mjtNum rate = mju_exp(-m->opt.timestep / mju_max(sim.ctrlnoiserate, mjMINVAL));
             mjtNum scale = sim.ctrlnoisestd * mju_sqrt(1-rate*rate);
 
             for (int i=0; i<m->nu; i++) {