diff --git a/.gitignore b/.gitignore
index 3c966caa..b7e6dfdb 100644
--- a/.gitignore
+++ b/.gitignore
@@ -11,3 +11,6 @@ doc/_build
 
 tenacity/_version.py
 /.pytest_cache
+venv/
+__pycache__/
+*.pyc
diff --git a/tenacity/wait.py b/tenacity/wait.py
index 6607e4fd..ccec4017 100644
--- a/tenacity/wait.py
+++ b/tenacity/wait.py
@@ -318,10 +318,14 @@ def __init__(
 
     @override
     def __call__(self, retry_state: "RetryCallState") -> float:
-        jitter = random.uniform(0, self.jitter)
+        #jitter = random.uniform(0, self.jitter)
         try:
             exp = self.exp_base ** (retry_state.attempt_number - 1)
-            result = self.multiplier * exp + jitter
+            result = self.multiplier * exp
         except OverflowError:
             result = self.max
+        # Subtract jitter width from max delay before adding jitter
+        # It prevents capped retries from syncing up at the same timestamp
+        result = min(result, max(0, self.max - self.jitter))
+        result += random.uniform(0, self.jitter)
         return max(max(0, self.min), min(result, self.max))
diff --git a/tests/test_tenacity.py b/tests/test_tenacity.py
index 95ab8117..ecaa54bf 100644
--- a/tests/test_tenacity.py
+++ b/tests/test_tenacity.py
@@ -671,14 +671,19 @@ def test_wait_exponential_jitter(self) -> None:
             self._assert_inclusive_range(fn(make_retry_state(4, 0)), 8, 9)
             self._assert_inclusive_range(fn(make_retry_state(5, 0)), 16, 17)
             self._assert_inclusive_range(fn(make_retry_state(6, 0)), 32, 33)
-            self.assertEqual(fn(make_retry_state(7, 0)), 60)
-            self.assertEqual(fn(make_retry_state(8, 0)), 60)
-            self.assertEqual(fn(make_retry_state(9, 0)), 60)
+            # Keep jitter active at the cap to prevent synchronized retries
+            self._assert_inclusive_range(fn(make_retry_state(7, 0)),59, 60)
+            self._assert_inclusive_range(fn(make_retry_state(8, 0)),59, 60)
+            self._assert_inclusive_range(fn(make_retry_state(9, 0)),59, 60)
 
         with self.assertWarns(DeprecationWarning):
             fn = tenacity.wait_exponential_jitter(10, 5)
-        for _ in range(1000):
-            self.assertEqual(fn(make_retry_state(1, 0)), 5)
+        results = {fn(make_retry_state(1, 0)) for _ in range(1000)}
+        # before this every call collapsed at max =5 but now it will spread across [4,5]
+        # which is [max-jitter, max]
+        self.assertGreater(len(results), 1)
+        for r in results:
+            self._assert_inclusive_range(r, 4, 5)
 
         # Default arguments exist
         fn = tenacity.wait_exponential_jitter()
@@ -705,7 +710,7 @@ def test_wait_exponential_jitter_timedelta(self) -> None:
         for _ in range(1000):
             self._assert_inclusive_range(fn(make_retry_state(1, 0)), 5, 5)
             self._assert_inclusive_range(fn(make_retry_state(5, 0)), 16, 17)
-            self.assertEqual(fn(make_retry_state(7, 0)), 60)
+            self._assert_inclusive_range(fn(make_retry_state(7, 0)), 59, 60)
 
     def test_wait_exponential_jitter_multiplier(self) -> None:
         fn = tenacity.wait_exponential_jitter(multiplier=10, max=60, jitter=0)