diff --git a/jax/_src/lax/linalg.py b/jax/_src/lax/linalg.py
index a63837ac9..1597c8c85 100644
--- a/jax/_src/lax/linalg.py
+++ b/jax/_src/lax/linalg.py
@@ -1607,18 +1607,19 @@ def _schur_cpu_lowering(ctx, operand, *, compute_schur_vectors, sort_eig_vals,
   operand_aval, = ctx.avals_in
   batch_dims = operand_aval.shape[:-2]
 
-  if sort_eig_vals:
-    T, vs, _sdim, info = lapack.gees_mhlo(
-        operand,
-        jobvs=compute_schur_vectors,
-        sort=sort_eig_vals,
-        select=select_callable)
-  else:
-    T, vs, info = lapack.gees_mhlo(
-        operand,
-        jobvs=compute_schur_vectors,
-        sort=sort_eig_vals,
-        select=select_callable)
+  # TODO(jakevdp): remove this try/except when minimum jaxlib >= 0.3.8
+  try:
+    gees_result = lapack.gees_mhlo(operand_aval.dtype, operand,
+                                   jobvs=compute_schur_vectors,
+                                   sort=sort_eig_vals,
+                                   select=select_callable)
+  except TypeError:  # API for jaxlib <= 0.3.7
+    gees_result = lapack.gees_mhlo(operand,  # pytype: disable=missing-parameter
+                                   jobvs=compute_schur_vectors,
+                                   sort=sort_eig_vals,
+                                   select=select_callable)
+  # Number of return values depends on value of sort_eig_vals.
+  T, vs, *_, info = gees_result
 
   ok = mlir.compare_mhlo(
       info, mlir.full_like_aval(0, ShapedArray(batch_dims, np.dtype(np.int32))),
diff --git a/jaxlib/lapack.py b/jaxlib/lapack.py
index 083385819..33caf5b21 100644
--- a/jaxlib/lapack.py
+++ b/jaxlib/lapack.py
@@ -672,7 +672,7 @@ def geev_mhlo(dtype, a, jobvl=True, jobvr=True):
 
 # # gees : Schur factorization
 
-def gees_mhlo(a, jobvs=True, sort=False, select=None):
+def gees_mhlo(dtype, a, jobvs=True, sort=False, select=None):
   a_type = ir.RankedTensorType(a.type)
   etype = a_type.element_type
   dims = a_type.shape
@@ -695,10 +695,19 @@ def gees_mhlo(a, jobvs=True, sort=False, select=None):
   jobvs = ord('V' if jobvs else 'N')
   sort = ord('S' if sort else 'N')
 
-  if not ir.ComplexType.isinstance(etype):
-    fn = "lapack_sgees" if etype == ir.F32Type.get() else "lapack_dgees"
-    schurvecs_type = etype
-    workspaces = [ir.RankedTensorType.get(dims, schurvecs_type)]
+  if dtype == np.float32:
+    fn = "lapack_sgees"
+  elif dtype == np.float64:
+    fn = "lapack_dgees"
+  elif dtype == np.complex64:
+    fn = "lapack_cgees"
+  elif dtype == np.complex128:
+    fn = "lapack_zgees"
+  else:
+    raise NotImplementedError(f"Unsupported dtype {dtype}")
+
+  if not np.issubdtype(dtype, np.complexfloating):
+    workspaces = [ir.RankedTensorType.get(dims, etype)]
     workspace_layouts = [layout]
     eigvals = [ir.RankedTensorType.get(batch_dims + (n,), etype)] * 2
     eigvals_layouts = [
@@ -706,11 +715,8 @@ def gees_mhlo(a, jobvs=True, sort=False, select=None):
                                     type=ir.IndexType.get())
     ] * 2
   else:
-    fn = ("lapack_cgees" if etype == ir.ComplexType.get(ir.F32Type.get())
-          else "lapack_zgees")
-    schurvecs_type = etype
     workspaces = [
-        ir.RankedTensorType.get(dims, schurvecs_type),
+        ir.RankedTensorType.get(dims, etype),
         ir.RankedTensorType.get([n], ir.ComplexType(etype).element_type),
     ]
     workspace_layouts = [
@@ -729,7 +735,7 @@ def gees_mhlo(a, jobvs=True, sort=False, select=None):
                                               type=ir.IndexType.get())
   out = mhlo.CustomCallOp(
       [ir.TupleType.get_tuple(workspaces + eigvals + [
-        ir.RankedTensorType.get(dims, schurvecs_type),
+        ir.RankedTensorType.get(dims, etype),
         ir.RankedTensorType.get(batch_dims, i32_type),
         ir.RankedTensorType.get(batch_dims, i32_type),
       ])],
diff --git a/tests/linalg_test.py b/tests/linalg_test.py
index 575954774..f676092f1 100644
--- a/tests/linalg_test.py
+++ b/tests/linalg_test.py
@@ -41,6 +41,8 @@ T = lambda x: np.swapaxes(x, -1, -2)
 float_types = jtu.dtypes.floating
 complex_types = jtu.dtypes.complex
 
+jaxlib_version = tuple(map(int, jax.lib.__version__.split('.')))
+
 
 class NumpyLinalgTest(jtu.JaxTestCase):
 
@@ -719,6 +721,19 @@ class NumpyLinalgTest(jtu.JaxTestCase):
       qr = partial(jnp.linalg.qr, mode=mode)
       jtu.check_jvp(qr, partial(jvp, qr), (a,), atol=3e-3)
 
+  @unittest.skipIf(jaxlib_version < (0, 3, 8), "test requires jaxlib>=0.3.8")
+  @jtu.skip_on_devices("tpu")
+  def testQrInvalidDtypeCPU(self, shape=(5, 6), dtype=np.float16):
+    # Regression test for https://github.com/google/jax/issues/10530
+    rng = jtu.rand_default(self.rng())
+    arr = rng(shape, dtype)
+    if jtu.device_under_test() == 'cpu':
+      err, msg = NotImplementedError, "Unsupported dtype float16"
+    else:
+      err, msg = ValueError, r"Unsupported dtype dtype\('float16'\)"
+    with self.assertRaisesRegex(err, msg):
+      jnp.linalg.qr(arr)
+
   @parameterized.named_parameters(jtu.cases_from_list(
       {"testcase_name": "_shape={}".format(
           jtu.format_shape_dtype_string(shape, dtype)),