diff --git a/tests/BUILD b/tests/BUILD
index efdd8265d..f957810e9 100644
--- a/tests/BUILD
+++ b/tests/BUILD
@@ -318,6 +318,9 @@ jax_test(
 jax_test(
     name = "lax_numpy_test",
     srcs = ["lax_numpy_test.py"],
+    backend_tags = {
+        "tpu": ["noasan"],  # Test times out.
+    },
     pjrt_c_api_bypass = True,
     shard_count = {
         "cpu": 40,
@@ -449,6 +452,9 @@ jax_test(
 jax_test(
     name = "lax_vmap_test",
     srcs = ["lax_vmap_test.py"],
+    backend_tags = {
+        "tpu": ["noasan"],  # Test times out.
+    },
     shard_count = {
         "cpu": 40,
         "gpu": 40,
@@ -606,6 +612,7 @@ jax_test(
         "tpu": 30,
         "iree": 30,
     },
+    tags = ["noasan"],  # Times out
 )
 
 # TODO(b/199564969): remove once we always enable_custom_prng
@@ -614,7 +621,10 @@ jax_test(
     srcs = ["random_test.py"],
     args = ["--jax_enable_custom_prng=true"],
     backend_tags = {
-        "cpu": ["noasan"],  # Times out under asan.
+        "cpu": [
+            "noasan",
+            "notsan",
+        ],  # Times out under asan/tsan.
     },
     main = "random_test.py",
     shard_count = {
@@ -675,6 +685,10 @@ jax_test(
         "tpu": 40,
         "iree": 10,
     },
+    tags = [
+        "noasan",
+        "notsan",
+    ],  # Times out
 )
 
 jax_test(
@@ -682,9 +696,7 @@ jax_test(
     srcs = ["sparse_test.py"],
     args = ["--jax_bcoo_cusparse_lowering=true"],
     backend_tags = {
-        "cpu": [
-            "noasan",  # Test times out under asan.
-        ],
+        "cpu": ["notsan"],  # Times out
         "tpu": ["optonly"],
     },
     shard_count = {
@@ -693,6 +705,7 @@ jax_test(
         "tpu": 50,
         "iree": 10,
     },
+    tags = ["noasan"],  # Test times out under asan.
     deps = [
         "//jax:experimental_sparse",
     ] + py_deps("scipy"),