diff --git a/tests/random_test.py b/tests/random_test.py
index 33027da6f5a4..a1e6e4e4c013 100644
--- a/tests/random_test.py
+++ b/tests/random_test.py
@@ -246,8 +246,8 @@ def testBernoulli(self, p, dtype):
     for (p, axis) in [
         ([.25] * 4, -1),
         ([.1, .2, .3, .4], -1),
-        ([[.25, .25], [.1, .9]], 1),
-        ([[.25, .1], [.25, .9]], 0),
+        ([[.5, .5], [.1, .9]], 1),
+        ([[.5, .1], [.5, .9]], 0),
     ]
     for sample_shape in [(10000,), (5000, 2)]
     for dtype in [onp.float32, onp.float64]))
@@ -255,25 +255,24 @@ def testCategorical(self, p, axis, dtype, sample_shape):
     key = random.PRNGKey(0)
     p = onp.array(p, dtype=dtype)
     logits = onp.log(p) - 42 # test unnormalized
-    shape = sample_shape + tuple(onp.delete(logits.shape, axis))
+    out_shape = tuple(onp.delete(logits.shape, axis))
+    shape = sample_shape + out_shape
     rand = lambda key, p: random.categorical(key, logits, shape=shape, axis=axis)
     crand = api.jit(rand)
 
     uncompiled_samples = rand(key, p)
     compiled_samples = crand(key, p)
 
-    if p.ndim > 1:
-      self.skipTest("multi-dimensional categorical tests are currently broken!")
+    if axis < 0:
+      axis += len(logits.shape)
 
     for samples in [uncompiled_samples, compiled_samples]:
-      if axis < 0:
-       axis += len(logits.shape)
-
       assert samples.shape == shape
-
+      samples = np.reshape(samples, (10000,) + out_shape)
       if len(p.shape[:-1]) > 0:
-        for cat_index, p_ in enumerate(p):
-          self._CheckChiSquared(samples[:, cat_index], pmf=lambda x: p_[x])
+        ps = onp.transpose(p, (1, 0)) if axis == 0 else p
+        for cat_samples, cat_p in zip(samples.transpose(), ps):
+          self._CheckChiSquared(cat_samples, pmf=lambda x: cat_p[x])
       else:
         self._CheckChiSquared(samples, pmf=lambda x: p[x])