diff --git a/tests/test_downloadermiddleware_httpcompression.py b/tests/test_downloadermiddleware_httpcompression.py
index f74fff218be..9deb81c37d1 100644
--- a/tests/test_downloadermiddleware_httpcompression.py
+++ b/tests/test_downloadermiddleware_httpcompression.py
@@ -402,6 +402,10 @@ def test_compression_bomb_setting_gzip(self):
         self._test_compression_bomb_setting("gzip")
 
     def test_compression_bomb_setting_zstd(self):
+        try:
+            import zstandard  # noqa: F401
+        except ImportError:
+            raise SkipTest("no zstd support (zstandard)")
         self._test_compression_bomb_setting("zstd")
 
     def _test_compression_bomb_spider_attr(self, compression_id):
@@ -436,6 +440,10 @@ def test_compression_bomb_spider_attr_gzip(self):
         self._test_compression_bomb_spider_attr("gzip")
 
     def test_compression_bomb_spider_attr_zstd(self):
+        try:
+            import zstandard  # noqa: F401
+        except ImportError:
+            raise SkipTest("no zstd support (zstandard)")
         self._test_compression_bomb_spider_attr("zstd")
 
     def _test_compression_bomb_request_meta(self, compression_id):
@@ -468,6 +476,10 @@ def test_compression_bomb_request_meta_gzip(self):
         self._test_compression_bomb_request_meta("gzip")
 
     def test_compression_bomb_request_meta_zstd(self):
+        try:
+            import zstandard  # noqa: F401
+        except ImportError:
+            raise SkipTest("no zstd support (zstandard)")
         self._test_compression_bomb_request_meta("zstd")
 
     def _test_download_warnsize_setting(self, compression_id):
@@ -510,6 +522,10 @@ def test_download_warnsize_setting_gzip(self):
         self._test_download_warnsize_setting("gzip")
 
     def test_download_warnsize_setting_zstd(self):
+        try:
+            import zstandard  # noqa: F401
+        except ImportError:
+            raise SkipTest("no zstd support (zstandard)")
         self._test_download_warnsize_setting("zstd")
 
     def _test_download_warnsize_spider_attr(self, compression_id):
@@ -554,6 +570,10 @@ def test_download_warnsize_spider_attr_gzip(self):
         self._test_download_warnsize_spider_attr("gzip")
 
     def test_download_warnsize_spider_attr_zstd(self):
+        try:
+            import zstandard  # noqa: F401
+        except ImportError:
+            raise SkipTest("no zstd support (zstandard)")
         self._test_download_warnsize_spider_attr("zstd")
 
     def _test_download_warnsize_request_meta(self, compression_id):
@@ -596,6 +616,10 @@ def test_download_warnsize_request_meta_gzip(self):
         self._test_download_warnsize_request_meta("gzip")
 
     def test_download_warnsize_request_meta_zstd(self):
+        try:
+            import zstandard  # noqa: F401
+        except ImportError:
+            raise SkipTest("no zstd support (zstandard)")
         self._test_download_warnsize_request_meta("zstd")
 
 
diff --git a/tests/test_utils_response.py b/tests/test_utils_response.py
index db3c31b8959..37ef89e76c4 100644
--- a/tests/test_utils_response.py
+++ b/tests/test_utils_response.py
@@ -204,7 +204,7 @@ def check_base_url(burl):
         ), "Inject unique base url with conditional comment"
 
     def test_open_in_browser_redos_comment(self):
-        MAX_CPU_TIME = 0.001
+        MAX_CPU_TIME = 0.02
 
         # Exploit input from
         # https://makenowjust-labs.github.io/recheck/playground/
@@ -221,7 +221,7 @@ def test_open_in_browser_redos_comment(self):
         self.assertLess(end_time - start_time, MAX_CPU_TIME)
 
     def test_open_in_browser_redos_head(self):
-        MAX_CPU_TIME = 0.001
+        MAX_CPU_TIME = 0.02
 
         # Exploit input from
         # https://makenowjust-labs.github.io/recheck/playground/