diff --git a/swh/model/hypothesis_strategies.py b/swh/model/hypothesis_strategies.py
--- a/swh/model/hypothesis_strategies.py
+++ b/swh/model/hypothesis_strategies.py
@@ -6,8 +6,9 @@
 import attr
 import datetime
 
+from hypothesis import assume
 from hypothesis.strategies import (
-    binary, builds, characters, composite, dictionaries,
+    binary, booleans, builds, characters, composite, dictionaries,
     from_regex, integers, just, lists, none, one_of,
     sampled_from, sets, text, tuples,
 )
@@ -65,11 +66,17 @@
         microseconds=integers(0, 1000000))
 
 
-def timestamps_with_timezone():
-    return builds(
-        TimestampWithTimezone,
+@composite
+def timestamps_with_timezone(
+        draw,
         timestamp=timestamps(),
-        offset=integers(min_value=-14*60, max_value=14*60))
+        offset=integers(min_value=-14*60, max_value=14*60),
+        negative_utc=booleans()):
+    assume(negative_utc and not offset)
+    return TimestampWithTimezone(
+        timestamp=timestamp,
+        offset=offset,
+        negative_utc=negative_utc)
 
 
 def origins():
diff --git a/swh/model/model.py b/swh/model/model.py
--- a/swh/model/model.py
+++ b/swh/model/model.py
@@ -176,6 +176,11 @@
             # you'll find in the wild...
             raise ValueError('offset too large: %d minutes' % value)
 
+    @negative_utc.validator
+    def check_negative_utc(self, attribute, value):
+        if self.offset and value:
+            raise ValueError("negative_utc can only be True is offset=0")
+
     @classmethod
     def from_dict(cls, obj: Union[Dict, datetime.datetime, int]):
         """Builds a TimestampWithTimezone from any of the formats
diff --git a/swh/model/tests/test_model.py b/swh/model/tests/test_model.py
--- a/swh/model/tests/test_model.py
+++ b/swh/model/tests/test_model.py
@@ -90,6 +90,69 @@
         Timestamp(seconds=0, microseconds=-1)
 
 
+def test_timestampwithtimezone():
+    ts = Timestamp(seconds=0, microseconds=0)
+    tstz = TimestampWithTimezone(
+        timestamp=ts,
+        offset=0,
+        negative_utc=False)
+    attr.validate(tstz)
+    assert tstz.negative_utc is False
+
+    attr.validate(TimestampWithTimezone(
+        timestamp=ts,
+        offset=10,
+        negative_utc=False))
+
+    attr.validate(TimestampWithTimezone(
+        timestamp=ts,
+        offset=-10,
+        negative_utc=False))
+
+    tstz = TimestampWithTimezone(
+        timestamp=ts,
+        offset=0,
+        negative_utc=True)
+    attr.validate(tstz)
+    assert tstz.negative_utc is True
+
+    with pytest.raises(AttributeTypeError):
+        TimestampWithTimezone(
+            timestamp=datetime.datetime.now(),
+            offset=0,
+            negative_utc=False)
+
+    with pytest.raises(AttributeTypeError):
+        TimestampWithTimezone(
+            timestamp=ts,
+            offset='0',
+            negative_utc=False)
+
+    with pytest.raises(AttributeTypeError):
+        TimestampWithTimezone(
+            timestamp=ts,
+            offset=1.0,
+            negative_utc=False)
+
+    with pytest.raises(AttributeTypeError):
+        TimestampWithTimezone(
+            timestamp=ts,
+            offset=1,
+            negative_utc=0)
+
+    with pytest.raises(ValueError):
+        TimestampWithTimezone(
+            timestamp=ts,
+            offset=1,
+            negative_utc=True)
+
+    with pytest.raises(ValueError):
+        TimestampWithTimezone(
+            timestamp=ts,
+            offset=-1,
+            negative_utc=True)
+
+
 def test_timestampwithtimezone_from_datetime():
     tz = datetime.timezone(datetime.timedelta(minutes=+60))
     date = datetime.datetime(