diff --git a/arrow/parser.py b/arrow/parser.py
index fc3774b09..c44b5fef6 100644
--- a/arrow/parser.py
+++ b/arrow/parser.py
@@ -713,10 +713,7 @@ def _build_datetime(parts: _Parts) -> datetime:
                 # day not given, default to 1
                 _day = 1
 
-            date_string = f"{year}-{week}-{_day}"
-
-            #  tokens for ISO 8601 weekdates
-            dt = datetime.strptime(date_string, "%G-%V-%u")
+            dt = datetime.fromisocalendar(year, week, _day)
 
             parts["year"] = dt.year
             parts["month"] = dt.month
diff --git a/arrow/util.py b/arrow/util.py
index 7171d92cc..ea4a2fb53 100644
--- a/arrow/util.py
+++ b/arrow/util.py
@@ -95,13 +95,7 @@ def iso_to_gregorian(iso_year: int, iso_week: int, iso_day: int) -> datetime.dat
     if not 1 <= iso_day <= 7:
         raise ValueError("ISO Calendar day value must be between 1-7")
 
-    # The first week of the year always contains 4 Jan.
-    fourth_jan = datetime.date(iso_year, 1, 4)
-    delta = datetime.timedelta(fourth_jan.isoweekday() - 1)
-    year_start = fourth_jan - delta
-    gregorian = year_start + datetime.timedelta(days=iso_day - 1, weeks=iso_week - 1)
-
-    return gregorian
+    return datetime.date.fromisocalendar(iso_year, iso_week, iso_day)
 
 
 def validate_bounds(bounds: str) -> None:
diff --git a/tests/test_factory.py b/tests/test_factory.py
index 056cee412..b1981ca86 100644
--- a/tests/test_factory.py
+++ b/tests/test_factory.py
@@ -236,6 +236,11 @@ def test_one_arg_iso_calendar(self):
         with pytest.raises(ValueError):
             self.factory.get((2014, 7, 10))
 
+    @pytest.mark.parametrize("year", [2014, 2019, 2021])
+    def test_one_arg_iso_calendar_invalid_week(self, year):
+        with pytest.raises(ValueError):
+            self.factory.get((year, 53, 1))
+
     def test_one_arg_other(self):
         with pytest.raises(TypeError):
             self.factory.get(object())
diff --git a/tests/test_parser.py b/tests/test_parser.py
index 7038d880f..9b0c61491 100644
--- a/tests/test_parser.py
+++ b/tests/test_parser.py
@@ -752,6 +752,22 @@ def test_parse_W(self):
             with pytest.raises(ParserError):
                 self.parser.parse(fmt, "W")
 
+    @pytest.mark.parametrize(
+        "value, expected",
+        [
+            ("0001-W01-1", datetime(1, 1, 1)),
+            ("0099-W01-1", datetime(98, 12, 29)),
+            ("0999-W01-1", datetime(998, 12, 31)),
+        ],
+    )
+    def test_parse_W_early_year(self, value, expected):
+        assert self.parser.parse(value, "W") == expected
+
+    @pytest.mark.parametrize("year", [2014, 2019, 2021])
+    def test_parse_W_invalid_week(self, year):
+        with pytest.raises(ValueError):
+            self.parser.parse(f"{year}-W53-1", "W")
+
     def test_parse_normalize_whitespace(self):
         assert self.parser.parse(
             "Jun 1 2005  1:33PM", "MMM D YYYY H:mmA", normalize_whitespace=True