diff --git a/stix2/test/test_utils.py b/stix2/test/test_utils.py
index a70853c..dbc0ed5 100644
--- a/stix2/test/test_utils.py
+++ b/stix2/test/test_utils.py
@@ -15,11 +15,33 @@ eastern = pytz.timezone('US/Eastern')
     (amsterdam.localize(dt.datetime(2017, 1, 1)), '2016-12-31T23:00:00Z'),
     (eastern.localize(dt.datetime(2017, 1, 1, 12, 34, 56)), '2017-01-01T17:34:56Z'),
     (eastern.localize(dt.datetime(2017, 7, 1)), '2017-07-01T04:00:00Z'),
+    (dt.datetime(2017, 7, 1), '2017-07-01T00:00:00Z'),
+    (dt.datetime(2017, 7, 1, 0, 0, 0, 1), '2017-07-01T00:00:00.000001Z'),
 ])
 def test_timestamp_formatting(dttm, timestamp):
     assert stix2.utils.format_datetime(dttm) == timestamp
 
 
+@pytest.mark.parametrize('timestamp, dttm', [
+    (dt.datetime(2017, 1, 1, 0, tzinfo=pytz.utc), dt.datetime(2017, 1, 1, 0, 0, 0, tzinfo=pytz.utc)),
+    (dt.date(2017, 1, 1), dt.datetime(2017, 1, 1, 0, 0, 0, tzinfo=pytz.utc)),
+    ('2017-01-01T00:00:00Z', dt.datetime(2017, 1, 1, 0, 0, 0, tzinfo=pytz.utc)),
+    ('2017-01-01T02:00:00+2:00', dt.datetime(2017, 1, 1, 0, 0, 0, tzinfo=pytz.utc)),
+    ('2017-01-01T00:00:00', dt.datetime(2017, 1, 1, 0, 0, 0, tzinfo=pytz.utc)),
+])
+def test_parse_datetime(timestamp, dttm):
+    assert stix2.utils.parse_into_datetime(timestamp) == dttm
+
+
+@pytest.mark.parametrize('ts', [
+    'foobar',
+    1,
+])
+def test_parse_datetime_invalid(ts):
+    with pytest.raises(ValueError):
+        stix2.utils.parse_into_datetime('foobar')
+
+
 @pytest.mark.parametrize('data', [
     {"a": 1},
     '{"a": 1}',
diff --git a/stix2/utils.py b/stix2/utils.py
index 6776681..bb41937 100644
--- a/stix2/utils.py
+++ b/stix2/utils.py
@@ -23,11 +23,11 @@ def format_datetime(dttm):
     # 4. Add subsecond value if non-zero
     # 5. Add "Z"
 
-    try:
-        zoned = dttm.astimezone(pytz.utc)
-    except ValueError:
+    if dttm.tzinfo is None or dttm.tzinfo.utcoffset(dttm) is None:
         # dttm is timezone-naive; assume UTC
-        pytz.utc.localize(dttm)
+        zoned = pytz.utc.localize(dttm)
+    else:
+        zoned = dttm.astimezone(pytz.utc)
     ts = zoned.strftime("%Y-%m-%dT%H:%M:%S")
     if zoned.microsecond > 0:
         ms = zoned.strftime("%f")
@@ -41,12 +41,12 @@ def parse_into_datetime(value):
             return value
         else:
             # Add a time component
-            return dt.datetime.combine(value, dt.time(), tzinfo=pytz.utc)
+            return dt.datetime.combine(value, dt.time(0, 0, tzinfo=pytz.utc))
 
     # value isn't a date or datetime object so assume it's a string
     try:
         parsed = parser.parse(value)
-    except TypeError:
+    except (TypeError, ValueError):
         # Unknown format
         raise ValueError("must be a datetime object, date object, or "
                          "timestamp string in a recognizable format.")