diff --git a/kafka/consumer/fetcher.py b/kafka/consumer/fetcher.py
index ebc6f6ba5..2600d7f69 100644
--- a/kafka/consumer/fetcher.py
+++ b/kafka/consumer/fetcher.py
@@ -1,4 +1,4 @@
-from __future__ import absolute_import
+from __future__ import absolute_import, division
 
 import collections
 import copy
@@ -246,7 +246,7 @@ def _reset_offset(self, partition):
         else:
             log.debug("Could not find offset for partition %s since it is probably deleted" % (partition,))
 
-    def _retrieve_offsets(self, timestamps, timeout_ms=float("inf")):
+    def _retrieve_offsets(self, timestamps, timeout_ms=None):
         """Fetch offset for each partition passed in ``timestamps`` map.
 
         Blocks until offsets are obtained, a non-retriable exception is raised
@@ -266,29 +266,38 @@ def _retrieve_offsets(self, timestamps, timeout_ms=float("inf")):
         if not timestamps:
             return {}
 
-        start_time = time.time()
-        remaining_ms = timeout_ms
+        elapsed = 0.0 # noqa: F841
+        begin = time.time()
+        def inner_timeout_ms(fallback=None):
+            if timeout_ms is None:
+                return fallback
+            elapsed = (time.time() - begin) * 1000
+            if elapsed >= timeout_ms:
+                raise Errors.KafkaTimeoutError('Timeout attempting to find coordinator')
+            ret = max(0, timeout_ms - elapsed)
+            if fallback is not None:
+                return min(ret, fallback)
+            return ret
+
         timestamps = copy.copy(timestamps)
-        while remaining_ms > 0:
+        while True:
             if not timestamps:
                 return {}
 
             future = self._send_list_offsets_requests(timestamps)
-            self._client.poll(future=future, timeout_ms=remaining_ms)
+            self._client.poll(future=future, timeout_ms=inner_timeout_ms())
 
             if future.succeeded():
                 return future.value
             if not future.retriable():
                 raise future.exception  # pylint: disable-msg=raising-bad-type
 
-            elapsed_ms = (time.time() - start_time) * 1000
-            remaining_ms = timeout_ms - elapsed_ms
-            if remaining_ms < 0:
-                break
-
             if future.exception.invalid_metadata:
                 refresh_future = self._client.cluster.request_update()
-                self._client.poll(future=refresh_future, timeout_ms=remaining_ms)
+                self._client.poll(future=refresh_future, timeout_ms=inner_timeout_ms())
+
+                if not future.is_done:
+                    break
 
                 # Issue #1780
                 # Recheck partition existence after after a successful metadata refresh
@@ -299,10 +308,7 @@ def _retrieve_offsets(self, timestamps, timeout_ms=float("inf")):
                         log.debug("Removed partition %s from offsets retrieval" % (unknown_partition, ))
                         timestamps.pop(unknown_partition)
             else:
-                time.sleep(self.config['retry_backoff_ms'] / 1000.0)
-
-            elapsed_ms = (time.time() - start_time) * 1000
-            remaining_ms = timeout_ms - elapsed_ms
+                time.sleep(inner_timeout_ms(self.config['retry_backoff_ms']) / 1000)
 
         raise Errors.KafkaTimeoutError(
             "Failed to get offsets by timestamps in %s ms" % (timeout_ms,))
diff --git a/kafka/coordinator/base.py b/kafka/coordinator/base.py
index 0d4aedb88..fa67b4ddd 100644
--- a/kafka/coordinator/base.py
+++ b/kafka/coordinator/base.py
@@ -245,13 +245,16 @@ def ensure_coordinator_ready(self, timeout_ms=None):
         """
         elapsed = 0.0 # noqa: F841
         begin = time.time()
-        def inner_timeout_ms():
+        def inner_timeout_ms(fallback=None):
             if timeout_ms is None:
-                return None
+                return fallback
             elapsed = (time.time() - begin) * 1000
             if elapsed >= timeout_ms:
                 raise Errors.KafkaTimeoutError('Timeout attempting to find coordinator')
-            return max(0, timeout_ms - elapsed)
+            ret = max(0, timeout_ms - elapsed)
+            if fallback is not None:
+                return min(ret, fallback)
+            return ret
 
         with self._client._lock, self._lock:
             while self.coordinator_unknown():
@@ -275,7 +278,7 @@ def inner_timeout_ms():
                             metadata_update = self._client.cluster.request_update()
                             self._client.poll(future=metadata_update, timeout_ms=inner_timeout_ms())
                         else:
-                            time.sleep(min(inner_timeout_ms(), self.config['retry_backoff_ms']) / 1000)
+                            time.sleep(inner_timeout_ms(self.config['retry_backoff_ms']) / 1000)
                     else:
                         raise future.exception  # pylint: disable-msg=raising-bad-type
 
@@ -369,13 +372,16 @@ def ensure_active_group(self, timeout_ms=None):
 
             elapsed = 0.0 # noqa: F841
             begin = time.time()
-            def inner_timeout_ms():
+            def inner_timeout_ms(fallback=None):
                 if timeout_ms is None:
-                    return None
+                    return fallback
                 elapsed = (time.time() - begin) * 1000
                 if elapsed >= timeout_ms:
-                    raise Errors.KafkaTimeoutError()
-                return max(0, timeout_ms - elapsed)
+                    raise Errors.KafkaTimeoutError('Timeout attempting to find coordinator')
+                ret = max(0, timeout_ms - elapsed)
+                if fallback is not None:
+                    return min(ret, fallback)
+                return ret
 
             while self.need_rejoin() or self._rejoin_incomplete():
                 self.ensure_coordinator_ready(timeout_ms=inner_timeout_ms())
@@ -399,7 +405,7 @@ def inner_timeout_ms():
                 while not self.coordinator_unknown():
                     if not self._client.in_flight_request_count(self.coordinator_id):
                         break
-                    self._client.poll(timeout_ms=min(200, inner_timeout_ms()))
+                    self._client.poll(timeout_ms=inner_timeout_ms(200))
                 else:
                     continue
 
@@ -451,7 +457,7 @@ def inner_timeout_ms():
                         continue
                     elif not future.retriable():
                         raise exception  # pylint: disable-msg=raising-bad-type
-                    time.sleep(min(inner_timeout_ms(), self.config['retry_backoff_ms']) / 1000)
+                    time.sleep(inner_timeout_ms(self.config['retry_backoff_ms']) / 1000)
 
     def _rejoin_incomplete(self):
         return self.join_future is not None