diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 6c91b6374b8af..c067adc8936a2 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -762,6 +762,7 @@ I/O
 - :func:`read_sas()` will correctly parse sas7bdat files with many columns (:issue:`22628`)
 - :func:`read_sas()` will correctly parse sas7bdat files with data page types having also bit 7 set (so page type is 128 + 256 = 384) (:issue:`16615`)
 - Bug in :meth:`detect_client_encoding` where potential ``IOError`` goes unhandled when importing in a mod_wsgi process due to restricted access to stdout. (:issue:`21552`)
+- Bug in :func:`to_string()` that broke column alignment when ``index=False`` and width of first column's values is greater than the width of first column's header (:issue:`16839`, :issue:`13032`)
 
 Plotting
 ^^^^^^^^
diff --git a/pandas/io/formats/format.py b/pandas/io/formats/format.py
index 1ff0613876838..db86409adc2b0 100644
--- a/pandas/io/formats/format.py
+++ b/pandas/io/formats/format.py
@@ -288,8 +288,7 @@ def to_string(self):
         if self.index:
             result = self.adj.adjoin(3, *[fmt_index[1:], fmt_values])
         else:
-            result = self.adj.adjoin(3, fmt_values).replace('\n ',
-                                                            '\n').strip()
+            result = self.adj.adjoin(3, fmt_values)
 
         if self.header and have_header:
             result = fmt_index[0] + '\n' + result
@@ -650,8 +649,6 @@ def to_string(self):
                 self._chk_truncate()
                 strcols = self._to_str_columns()
                 text = self.adj.adjoin(1, *strcols)
-        if not self.index:
-            text = text.replace('\n ', '\n').strip()
         self.buf.writelines(text)
 
         if self.should_show_dimensions:
diff --git a/pandas/tests/io/formats/test_format.py b/pandas/tests/io/formats/test_format.py
index ffbc978b92ba5..03e830fb09ad6 100644
--- a/pandas/tests/io/formats/test_format.py
+++ b/pandas/tests/io/formats/test_format.py
@@ -1269,18 +1269,42 @@ def test_to_string_specified_header(self):
             df.to_string(header=['X'])
 
     def test_to_string_no_index(self):
-        df = DataFrame({'x': [1, 2, 3], 'y': [4, 5, 6]})
+        # GH 16839, GH 13032
+        df = DataFrame({'x': [11, 22], 'y': [33, -44], 'z': ['AAA', '   ']})
 
         df_s = df.to_string(index=False)
-        expected = "x  y\n1  4\n2  5\n3  6"
+        # Leading space is expected for positive numbers.
+        expected = ("  x   y    z\n"
+                    " 11  33  AAA\n"
+                    " 22 -44     ")
+        assert df_s == expected
 
+        df_s = df[['y', 'x', 'z']].to_string(index=False)
+        expected = ("  y   x    z\n"
+                    " 33  11  AAA\n"
+                    "-44  22     ")
         assert df_s == expected
 
     def test_to_string_line_width_no_index(self):
+        # GH 13998, GH 22505
         df = DataFrame({'x': [1, 2, 3], 'y': [4, 5, 6]})
 
         df_s = df.to_string(line_width=1, index=False)
-        expected = "x  \\\n1   \n2   \n3   \n\ny  \n4  \n5  \n6"
+        expected = " x  \\\n 1   \n 2   \n 3   \n\n y  \n 4  \n 5  \n 6  "
+
+        assert df_s == expected
+
+        df = DataFrame({'x': [11, 22, 33], 'y': [4, 5, 6]})
+
+        df_s = df.to_string(line_width=1, index=False)
+        expected = "  x  \\\n 11   \n 22   \n 33   \n\n y  \n 4  \n 5  \n 6  "
+
+        assert df_s == expected
+
+        df = DataFrame({'x': [11, 22, -33], 'y': [4, 5, -6]})
+
+        df_s = df.to_string(line_width=1, index=False)
+        expected = "  x  \\\n 11   \n 22   \n-33   \n\n y  \n 4  \n 5  \n-6  "
 
         assert df_s == expected
 
@@ -1793,7 +1817,7 @@ def test_to_string_without_index(self):
         # GH 11729 Test index=False option
         s = Series([1, 2, 3, 4])
         result = s.to_string(index=False)
-        expected = (u('1\n') + '2\n' + '3\n' + '4')
+        expected = (u(' 1\n') + ' 2\n' + ' 3\n' + ' 4')
         assert result == expected
 
     def test_unicode_name_in_footer(self):