diff --git a/storage/google/cloud/storage/blob.py b/storage/google/cloud/storage/blob.py
index 0e726c42f0f2..9c89c52b9e24 100644
--- a/storage/google/cloud/storage/blob.py
+++ b/storage/google/cloud/storage/blob.py
@@ -298,7 +298,7 @@ def public_url(self):
         return "{storage_base_url}/{bucket_name}/{quoted_name}".format(
             storage_base_url=_API_ACCESS_ENDPOINT,
             bucket_name=self.bucket.name,
-            quoted_name=quote(self.name.encode("utf-8")),
+            quoted_name=_quote(self.name, safe=b"/~"),
         )
 
     def generate_signed_url(
@@ -416,8 +416,9 @@ def generate_signed_url(
         elif version not in ("v2", "v4"):
             raise ValueError("'version' must be either 'v2' or 'v4'")
 
+        quoted_name = _quote(self.name, safe=b"/~")
         resource = "/{bucket_name}/{quoted_name}".format(
-            bucket_name=self.bucket.name, quoted_name=quote(self.name.encode("utf-8"))
+            bucket_name=self.bucket.name, quoted_name=quoted_name
         )
 
         if credentials is None:
@@ -1983,7 +1984,7 @@ def _get_encryption_headers(key, source=False):
     }
 
 
-def _quote(value):
+def _quote(value, safe=b"~"):
     """URL-quote a string.
 
     If the value is unicode, this method first UTF-8 encodes it as bytes and
@@ -1994,11 +1995,14 @@ def _quote(value):
     :type value: str or bytes
     :param value: The value to be URL-quoted.
 
+    :type safe: bytes
+    :param safe: Bytes *not* to be quoted.  By default, includes only ``b'~'``.
+
     :rtype: str
     :returns: The encoded value (bytes in Python 2, unicode in Python 3).
     """
     value = _to_bytes(value, encoding="utf-8")
-    return quote(value, safe="")
+    return quote(value, safe=safe)
 
 
 def _maybe_rewind(stream, rewind=False):
diff --git a/storage/tests/unit/test_blob.py b/storage/tests/unit/test_blob.py
index aeb38b428f05..b264ddcb8acf 100644
--- a/storage/tests/unit/test_blob.py
+++ b/storage/tests/unit/test_blob.py
@@ -344,6 +344,14 @@ def test_public_url_w_slash_in_name(self):
             blob.public_url, "https://storage.googleapis.com/name/parent/child"
         )
 
+    def test_public_url_w_tilde_in_name(self):
+        BLOB_NAME = "foo~bar"
+        bucket = _Bucket()
+        blob = self._make_one(BLOB_NAME, bucket=bucket)
+        self.assertEqual(
+            blob.public_url, "https://storage.googleapis.com/name/foo~bar"
+        )
+
     def test_public_url_with_non_ascii(self):
         blob_name = u"winter \N{snowman}"
         bucket = _Bucket()
@@ -426,7 +434,7 @@ def _generate_signed_url_helper(
             expected_creds = credentials
 
         encoded_name = blob_name.encode("utf-8")
-        expected_resource = "/name/{}".format(parse.quote(encoded_name))
+        expected_resource = "/name/{}".format(parse.quote(encoded_name, safe=b"/~"))
         expected_kwargs = {
             "resource": expected_resource,
             "expiration": expiration,
@@ -466,6 +474,10 @@ def test_generate_signed_url_v2_w_slash_in_name(self):
         BLOB_NAME = "parent/child"
         self._generate_signed_url_v2_helper(blob_name=BLOB_NAME)
 
+    def test_generate_signed_url_v2_w_tilde_in_name(self):
+        BLOB_NAME = "foo~bar"
+        self._generate_signed_url_v2_helper(blob_name=BLOB_NAME)
+
     def test_generate_signed_url_v2_w_endpoint(self):
         self._generate_signed_url_v2_helper(
             api_access_endpoint="https://api.example.com/v1"
@@ -514,6 +526,10 @@ def test_generate_signed_url_v4_w_slash_in_name(self):
         BLOB_NAME = "parent/child"
         self._generate_signed_url_v4_helper(blob_name=BLOB_NAME)
 
+    def test_generate_signed_url_v4_w_tilde_in_name(self):
+        BLOB_NAME = "foo~bar"
+        self._generate_signed_url_v4_helper(blob_name=BLOB_NAME)
+
     def test_generate_signed_url_v4_w_endpoint(self):
         self._generate_signed_url_v4_helper(
             api_access_endpoint="https://api.example.com/v1"
@@ -3119,10 +3135,10 @@ def test_updated_unset(self):
 
 class Test__quote(unittest.TestCase):
     @staticmethod
-    def _call_fut(value):
+    def _call_fut(*args, **kw):
         from google.cloud.storage.blob import _quote
 
-        return _quote(value)
+        return _quote(*args, **kw)
 
     def test_bytes(self):
         quoted = self._call_fut(b"\xDE\xAD\xBE\xEF")
@@ -3137,6 +3153,21 @@ def test_bad_type(self):
         with self.assertRaises(TypeError):
             self._call_fut(None)
 
+    def test_w_slash_default(self):
+        with_slash = "foo/bar/baz"
+        quoted = self._call_fut(with_slash)
+        self.assertEqual(quoted, "foo%2Fbar%2Fbaz")
+
+    def test_w_slash_w_safe(self):
+        with_slash = "foo/bar/baz"
+        quoted_safe = self._call_fut(with_slash, safe=b"/")
+        self.assertEqual(quoted_safe, with_slash)
+
+    def test_w_tilde(self):
+        with_tilde = "bam~qux"
+        quoted = self._call_fut(with_tilde, safe=b"~")
+        self.assertEqual(quoted, with_tilde)
+
 
 class Test__maybe_rewind(unittest.TestCase):
     @staticmethod