diff --git a/src/array_api_extra/testing.py b/src/array_api_extra/testing.py
index 4f8288cf..37e8e69e 100644
--- a/src/array_api_extra/testing.py
+++ b/src/array_api_extra/testing.py
@@ -39,7 +39,7 @@ def override(func: object) -> object:
 def lazy_xp_function(  # type: ignore[explicit-any]
     func: Callable[..., Any],
     *,
-    allow_dask_compute: int = 0,
+    allow_dask_compute: bool | int = False,
     jax_jit: bool = True,
     static_argnums: int | Sequence[int] | None = None,
     static_argnames: str | Iterable[str] | None = None,
@@ -59,9 +59,10 @@ def lazy_xp_function(  # type: ignore[explicit-any]
     ----------
     func : callable
         Function to be tested.
-    allow_dask_compute : int, optional
-        Number of times `func` is allowed to internally materialize the Dask graph. This
-        is typically triggered by ``bool()``, ``float()``, or ``np.asarray()``.
+    allow_dask_compute : bool | int, optional
+        Whether `func` is allowed to internally materialize the Dask graph, or maximum
+        number of times it is allowed to do so. This is typically triggered by
+        ``bool()``, ``float()``, or ``np.asarray()``.
 
         Set to 1 if you are aware that `func` converts the input parameters to NumPy and
         want to let it do so at least for the time being, knowing that it is going to be
@@ -75,7 +76,10 @@ def lazy_xp_function(  # type: ignore[explicit-any]
         a test function that invokes `func` multiple times should still work with this
         parameter set to 1.
 
-        Default: 0, meaning that `func` must be fully lazy and never materialize the
+        Set to True to allow `func` to materialize the graph an unlimited number
+        of times.
+
+        Default: False, meaning that `func` must be fully lazy and never materialize the
         graph.
     jax_jit : bool, optional
         Set to True to replace `func` with ``jax.jit(func)`` after calling the
@@ -235,6 +239,10 @@ def iter_tagged() -> (  # type: ignore[explicit-any]
     if is_dask_namespace(xp):
         for mod, name, func, tags in iter_tagged():
             n = tags["allow_dask_compute"]
+            if n is True:
+                n = 1_000_000
+            elif n is False:
+                n = 0
             wrapped = _dask_wrap(func, n)
             monkeypatch.setattr(mod, name, wrapped)
 
diff --git a/tests/test_testing.py b/tests/test_testing.py
index ff67121b..fb9ba581 100644
--- a/tests/test_testing.py
+++ b/tests/test_testing.py
@@ -130,13 +130,18 @@ def non_materializable4(x: Array) -> Array:
     return non_materializable(x)
 
 
+def non_materializable5(x: Array) -> Array:
+    return non_materializable(x)
+
+
 lazy_xp_function(good_lazy)
 # Works on JAX and Dask
 lazy_xp_function(non_materializable2, jax_jit=False, allow_dask_compute=2)
+lazy_xp_function(non_materializable3, jax_jit=False, allow_dask_compute=True)
 # Works on JAX, but not Dask
-lazy_xp_function(non_materializable3, jax_jit=False, allow_dask_compute=1)
+lazy_xp_function(non_materializable4, jax_jit=False, allow_dask_compute=1)
 # Works neither on Dask nor JAX
-lazy_xp_function(non_materializable4)
+lazy_xp_function(non_materializable5)
 
 
 def test_lazy_xp_function(xp: ModuleType):
@@ -147,29 +152,30 @@ def test_lazy_xp_function(xp: ModuleType):
     xp_assert_equal(non_materializable(x), xp.asarray([1.0, 2.0]))
     # Wrapping explicitly disabled
     xp_assert_equal(non_materializable2(x), xp.asarray([1.0, 2.0]))
+    xp_assert_equal(non_materializable3(x), xp.asarray([1.0, 2.0]))
 
     if is_jax_namespace(xp):
-        xp_assert_equal(non_materializable3(x), xp.asarray([1.0, 2.0]))
+        xp_assert_equal(non_materializable4(x), xp.asarray([1.0, 2.0]))
         with pytest.raises(
             TypeError, match="Attempted boolean conversion of traced array"
         ):
-            _ = non_materializable4(x)  # Wrapped
+            _ = non_materializable5(x)  # Wrapped
 
     elif is_dask_namespace(xp):
         with pytest.raises(
             AssertionError,
             match=r"dask\.compute.* 2 times, but only up to 1 calls are allowed",
         ):
-            _ = non_materializable3(x)
+            _ = non_materializable4(x)
         with pytest.raises(
             AssertionError,
             match=r"dask\.compute.* 1 times, but no calls are allowed",
         ):
-            _ = non_materializable4(x)
+            _ = non_materializable5(x)
 
     else:
-        xp_assert_equal(non_materializable3(x), xp.asarray([1.0, 2.0]))
         xp_assert_equal(non_materializable4(x), xp.asarray([1.0, 2.0]))
+        xp_assert_equal(non_materializable5(x), xp.asarray([1.0, 2.0]))
 
 
 def static_params(x: Array, n: int, flag: bool = False) -> Array: