diff --git a/test/test_adaptive_stepsize_controller.py b/test/test_adaptive_stepsize_controller.py
new file mode 100644
index 00000000..4f52123e
--- /dev/null
+++ b/test/test_adaptive_stepsize_controller.py
@@ -0,0 +1,67 @@
+import diffrax
+import jax.numpy as jnp
+
+
+def test_step_ts():
+    term = diffrax.ODETerm(lambda t, y, args: -0.2 * y)
+    solver = diffrax.Dopri5()
+    t0 = 0
+    t1 = 5
+    dt0 = None
+    y0 = 1.0
+    stepsize_controller = diffrax.PIDController(rtol=1e-4, atol=1e-6, step_ts=[3, 4])
+    saveat = diffrax.SaveAt(steps=True)
+    sol = diffrax.diffeqsolve(
+        term,
+        solver,
+        t0,
+        t1,
+        dt0,
+        y0,
+        stepsize_controller=stepsize_controller,
+        saveat=saveat,
+    )
+    assert 3 in sol.ts
+    assert 4 in sol.ts
+
+
+def test_jump_ts():
+    # Tests no regression of https://github.com/patrick-kidger/diffrax/issues/58
+
+    def vector_field(t, y, args):
+        x, v = y
+        force = jnp.where(t < 7.5, 10, -10)
+        return v, -4 * jnp.pi**2 * x - 4 * jnp.pi * 0.05 * v + force
+
+    term = diffrax.ODETerm(vector_field)
+    solver = diffrax.Dopri5()
+    t0 = 0
+    t1 = 15
+    dt0 = None
+    y0 = 1.5, 0
+    saveat = diffrax.SaveAt(steps=True)
+
+    def run(**kwargs):
+        stepsize_controller = diffrax.PIDController(rtol=1e-4, atol=1e-6, **kwargs)
+        return diffrax.diffeqsolve(
+            term,
+            solver,
+            t0,
+            t1,
+            dt0,
+            y0,
+            stepsize_controller=stepsize_controller,
+            saveat=saveat,
+        )
+
+    sol_no_jump_ts = run()
+    sol_with_jump_ts = run(jump_ts=[7.5])
+    assert sol_no_jump_ts.stats["num_steps"] > sol_with_jump_ts.stats["num_steps"]
+    assert sol_with_jump_ts.result == 0
+
+    sol = run(jump_ts=[7.5], step_ts=[7.5])
+    assert sol.result == 0
+    sol = run(jump_ts=[7.5], step_ts=[3.5, 8])
+    assert sol.result == 0
+    assert 3.5 in sol.ts
+    assert 8 in sol.ts
diff --git a/test/test_adjoint.py b/test/test_adjoint.py
index 6ab109c8..985fd907 100644
--- a/test/test_adjoint.py
+++ b/test/test_adjoint.py
@@ -123,7 +123,9 @@ def test_adjoint_seminorm():
 
     def solve(y0):
         adjoint = diffrax.BacksolveAdjoint(
-            stepsize_controller=diffrax.PIDController(norm=diffrax.adjoint_rms_seminorm)
+            stepsize_controller=diffrax.PIDController(
+                rtol=1e-3, atol=1e-6, norm=diffrax.adjoint_rms_seminorm
+            )
         )
         sol = diffrax.diffeqsolve(
             term,
diff --git a/test/test_solver.py b/test/test_solver.py
index 30879866..eb24d672 100644
--- a/test/test_solver.py
+++ b/test/test_solver.py
@@ -8,7 +8,7 @@ def test_half_solver():
     y0 = 1.0
     dt0 = None
     solver = diffrax.HalfSolver(diffrax.Euler())
-    stepsize_controller = diffrax.PIDController(rtl=1e-3, atol=1e-6)
+    stepsize_controller = diffrax.PIDController(rtol=1e-3, atol=1e-6)
     diffrax.diffeqsolve(
         term, solver, t0, t1, dt0, y0, stepsize_controller=stepsize_controller
     )