diff --git a/arrow/parser.py b/arrow/parser.py
index fc3774b09..05b255212 100644
--- a/arrow/parser.py
+++ b/arrow/parser.py
@@ -662,12 +662,21 @@ def _parse_token(
 
             # floating-point (IEEE-754) defaults to half-to-even rounding
             seventh_digit = int(value[6])
-            if seventh_digit == 5:
-                rounding = int(value[5]) % 2
-            elif seventh_digit > 5:
+            if seventh_digit > 5:
+                # Strictly above the half-way point, always round up.
                 rounding = 1
-            else:
+            elif seventh_digit < 5:
+                # Strictly below the half-way point, always round down.
                 rounding = 0
+            else:
+                # Exactly at the half-way point: only use round-half-to-even
+                # (banker's rounding) when the trailing digits are all zero.
+                # If anything non-zero follows the 5, the truncated value is
+                # strictly above the midpoint and we must round up.
+                if any(ch != "0" for ch in value[7:]):
+                    rounding = 1
+                else:
+                    rounding = int(value[5]) % 2
 
             parts["microsecond"] = int(value[:6]) + rounding
 
diff --git a/tests/test_parser.py b/tests/test_parser.py
index 7038d880f..8236c1c98 100644
--- a/tests/test_parser.py
+++ b/tests/test_parser.py
@@ -393,16 +393,29 @@ def test_parse_subsecond_rounding(self):
         assert self.parser.parse(string, datetime_format) == self.expected
         assert self.parser.parse_iso(string) == self.expected
 
-        # round half-up
+        # round up (non-zero trailing past 5)
         string = "2013-01-01 12:30:45.987653521"
         assert self.parser.parse(string, datetime_format) == self.expected
         assert self.parser.parse_iso(string) == self.expected
 
-        # round half-down
+        # round up (6th=4, non-zero trailing past 5) - 6th=4, 7th=5, trailing "210" non-zero,
+        # so the value is strictly above the half-way point and must round up
         string = "2013-01-01 12:30:45.9876545210"
+        expected_round_up = datetime(2013, 1, 1, 12, 30, 45, 987655)
+        assert self.parser.parse(string, datetime_format) == expected_round_up
+        assert self.parser.parse_iso(string) == expected_round_up
+
+        # round half-to-even (6th=3, exact .5) - 6th is odd, so round up to even
+        string = "2013-01-01 12:30:45.9876535"
         assert self.parser.parse(string, datetime_format) == self.expected
         assert self.parser.parse_iso(string) == self.expected
 
+        # round half-to-even (6th=4, exact .5) - 6th is even, so round down to even
+        string = "2013-01-01 12:30:45.9876545"
+        expected_half_to_even = datetime(2013, 1, 1, 12, 30, 45, 987654)
+        assert self.parser.parse(string, datetime_format) == expected_half_to_even
+        assert self.parser.parse_iso(string) == expected_half_to_even
+
     # overflow (zero out the subseconds and increment the seconds)
     # regression tests for issue #636
     def test_parse_subsecond_rounding_overflow(self):
@@ -1058,6 +1071,22 @@ def test_YYYY_MM_DDTHH_mm_ss_S(self):
             2013, 2, 3, 4, 5, 6, 789124
         )
 
+    def test_YYYY_MM_DDTHH_mm_ss_S_round_half_up(self):
+        # When the 7th digit is 5, the truncated value sits at the half-way
+        # point of the 6th digit. The value is strictly greater than the
+        # midpoint iff at least one trailing digit is non-zero, in which
+        # case we must round up rather than apply banker's rounding to
+        # the 6th digit.
+        # 6th digit even, 7th == 5, nothing trailing -> banker's rounds down
+        assert self.parser.parse_iso("2013-02-03T04:05:06.789124500") == datetime(
+            2013, 2, 3, 4, 5, 6, 789124
+        )
+        # 6th digit even, 7th == 5, non-zero digit after -> strictly above
+        # midpoint, must round up (was rounding down before the fix)
+        assert self.parser.parse_iso("2013-02-03T04:05:06.789124501") == datetime(
+            2013, 2, 3, 4, 5, 6, 789125
+        )
+
     def test_YYYY_MM_DDTHH_mm_ss_SZ(self):
         assert self.parser.parse_iso("2013-02-03T04:05:06.7+01:00") == datetime(
             2013, 2, 3, 4, 5, 6, 700000, tzinfo=tz.tzoffset(None, 3600)
@@ -1144,8 +1173,10 @@ def test_parse_subsecond(self):
     def test_gnu_date(self):
         """Regression tests for parsing output from GNU date."""
         # date -Ins
+        # 7th digit is 5, trailing "57" is non-zero, so the value is strictly
+        # above the half-way point and must round up from 895636 to 895637
         assert self.parser.parse_iso("2016-11-16T09:46:30,895636557-0800") == datetime(
-            2016, 11, 16, 9, 46, 30, 895636, tzinfo=tz.tzoffset(None, -3600 * 8)
+            2016, 11, 16, 9, 46, 30, 895637, tzinfo=tz.tzoffset(None, -3600 * 8)
         )
 
         # date --rfc-3339=ns