diff --git a/src/tablib/core.py b/src/tablib/core.py
index c46ddee4..2679fd24 100644
--- a/src/tablib/core.py
+++ b/src/tablib/core.py
@@ -74,6 +74,9 @@ def append(self, value):
     def insert(self, index, value):
         self._row.insert(index, value)
 
+    def copy(self):
+        return Row(self._row.copy(), self.tags.copy())
+
     def __contains__(self, item):
         return item in self._row
 
@@ -276,27 +279,25 @@ def _package(self, dicts=True, ordered=True):
         else:
             dict_pack = dict
 
-        # Execute formatters
-        if self._formatters:
-            for row_i, row in enumerate(_data):
+        def format_row(row):
+            # Execute formatters
+            if self._formatters:
+                row = row.copy()  # To not mutate internal data structure
                 for col, callback in self._formatters:
-                    try:
-                        if col is None:
-                            for j, c in enumerate(row):
-                                _data[row_i][j] = callback(c)
-                        else:
-                            _data[row_i][col] = callback(row[col])
-                    except IndexError:
-                        raise InvalidDatasetIndex
+                    if col is None:
+                        # Apply formatter to all cells
+                        row = [callback(cell) for cell in row]
+                    else:
+                        row[col] = callback(row[col])
+            return list(row)
 
         if self.headers:
             if dicts:
-                data = [dict_pack(list(zip(self.headers, data_row))) for data_row in _data]
+                data = [dict_pack(list(zip(self.headers, format_row(row)))) for row in _data]
             else:
-                data = [list(self.headers)] + list(_data)
+                data = [list(self.headers)] + [format_row(row) for row in _data]
         else:
-            data = [list(row) for row in _data]
-
+            data = [format_row(row) for row in _data]
         return data
 
     def _get_headers(self):
diff --git a/tests/test_tablib.py b/tests/test_tablib.py
index 9035c1e1..63f6d659 100755
--- a/tests/test_tablib.py
+++ b/tests/test_tablib.py
@@ -565,12 +565,18 @@ def test_formatters(self):
         """Confirm formatters are being triggered."""
 
         def _formatter(cell_value):
-            return str(cell_value).upper()
+            return str(cell_value)[1:]
 
         self.founders.add_formatter('last_name', _formatter)
 
-        for name in [r['last_name'] for r in self.founders.dict]:
-            self.assertTrue(name.isupper())
+        expected = [
+            {'first_name': 'John', 'last_name': 'dams', 'gpa': 90},
+            {'first_name': 'George', 'last_name': 'ashington', 'gpa': 67},
+            {'first_name': 'Thomas', 'last_name': 'efferson', 'gpa': 50},
+        ]
+        self.assertEqual(self.founders.dict, expected)
+        # Test once more as the result should be the same
+        self.assertEqual(self.founders.dict, expected)
 
     def test_unicode_renders_markdown_table(self):
         # add another entry to test right field width for