diff --git a/jax/numpy/lax_numpy.py b/jax/numpy/lax_numpy.py
index b7f3eaca6948..636bd5bcd901 100644
--- a/jax/numpy/lax_numpy.py
+++ b/jax/numpy/lax_numpy.py
@@ -1898,37 +1898,45 @@ def repeat(a, repeats, axis=None):
 
   return reshape(ret, new_shape)
 
+def _triangular_mask(n, m, k, tie_in=None):
+  x = arange(n, dtype=int32)
+  y = arange(m, dtype=int32)
+  if tie_in is not None:
+    x = lax.tie_in(tie_in, x)
+    y = lax.tie_in(tie_in, y)
+  return lax.ge(
+      (lax.broadcast_in_dim(x, shape=(n, m), broadcast_dimensions=(0,)) +
+       lax.convert_element_type(k, int32)),
+      lax.broadcast(y, [n]))
+
 @_wraps(onp.tri)
 def tri(N, M=None, k=0, dtype=None):
   lax._check_user_dtype_supported(dtype, "tri")
-  M = M if M is not None else N
-  dtype = dtype or float32
-  x = arange(N, dtype=int32)
-  y = arange(M, dtype=int32)
-  mask = lax.ge(
-      (lax.broadcast_in_dim(x, shape=(N, M), broadcast_dimensions=(0,)) +
-       int32(k)),
-      lax.broadcast(y, [N]))
-  return lax.convert_element_type(mask, dtype)
-
+  mask = _triangular_mask(N, M if M is not None else N, k)
+  return lax.convert_element_type(mask, dtype or float32)
 
-@_wraps(onp.tril)
-def tril(m, k=0):
+@jit
+def _tril(m, k=0):
   m_shape = shape(m)
   if len(m_shape) < 2:
     raise ValueError("Argument to jax.numpy.tril must be at least 2D")
-  mask = tri(*m_shape[-2:], k=k, dtype=bool)
+  mask = _triangular_mask(m_shape[-2], m_shape[-1], k, tie_in=m)
   return lax.select(lax.broadcast(mask, m_shape[:-2]), m, zeros_like(m))
 
+@_wraps(onp.tril)
+def tril(m, k=0): return _tril(m, k)
 
-@_wraps(onp.triu, update_doc=False)
-def triu(m, k=0):
+@jit
+def _triu(m, k):
   m_shape = shape(m)
   if len(m_shape) < 2:
     raise ValueError("Argument to jax.numpy.triu must be at least 2D")
-  mask = tri(*m_shape[-2:], k=k - 1, dtype=bool)
+  mask = _triangular_mask(m_shape[-2], m_shape[-1], k-1, tie_in=m)
   return lax.select(lax.broadcast(mask, m_shape[:-2]), zeros_like(m), m)
 
+@_wraps(onp.triu, update_doc=False)
+def triu(m, k=0): return _triu(m, k)
+
 
 @_wraps(onp.trace)
 def trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None):