diff --git a/babel/dates.py b/babel/dates.py
index 4bae3eaa0..26ccd120a 100644
--- a/babel/dates.py
+++ b/babel/dates.py
@@ -1319,9 +1319,7 @@ def format_era(self, char, num):
     def format_year(self, char, num):
         value = self.value.year
         if char.isupper():
-            week = self.get_week_number(self.get_day_of_year())
-            if week == 0:
-                value -= 1
+            value = self.value.isocalendar()[0]
         year = self.format(value, num)
         if num == 2:
             year = year[-2:]
@@ -1505,8 +1503,15 @@ def get_week_number(self, day_of_period, day_of_week=None):
         if first_day < 0:
             first_day += 7
         week_number = (day_of_period + first_day - 1) // 7
+
         if 7 - first_day >= self.locale.min_week_days:
             week_number += 1
+
+        if self.locale.first_week_day == 0:
+            max_weeks = date(year=self.value.year, day=28, month=12).isocalendar()[1]
+            if week_number > max_weeks:
+                week_number -= max_weeks
+
         return week_number
 
 
diff --git a/tests/test_dates.py b/tests/test_dates.py
index b8c293ba6..d77c0ea42 100644
--- a/tests/test_dates.py
+++ b/tests/test_dates.py
@@ -79,6 +79,15 @@ def test_week_of_year_last_us_extra_week(self):
         fmt = dates.DateTimeFormat(d, locale='en_US')
         self.assertEqual('53', fmt['w'])
 
+    def test_week_of_year_de_first_us_last_with_year(self):
+        d = date(2018,12,31)
+        fmt = dates.DateTimeFormat(d, locale='de_DE')
+        self.assertEqual('1', fmt['w'])
+        self.assertEqual('2019', fmt['YYYY'])
+        fmt = dates.DateTimeFormat(d, locale='en_US')
+        self.assertEqual('53', fmt['w'])
+        self.assertEqual('2018',fmt['yyyy'])
+
     def test_week_of_month_first(self):
         d = date(2006, 1, 8)
         fmt = dates.DateTimeFormat(d, locale='de_DE')