diff --git a/Doc/library/csv.rst b/Doc/library/csv.rst
index 7a72c26d5ba..cb03f8da202 100644
--- a/Doc/library/csv.rst
+++ b/Doc/library/csv.rst
@@ -269,6 +269,20 @@ The :mod:`csv` module defines the following classes:
 
       Analyze the sample text (presumed to be in CSV format) and return
       :const:`True` if the first row appears to be a series of column headers.
+      Inspecting each column, one of two key criteria will be considered to
+      estimate if the sample contains a header:
+
+        - the second through n-th rows contain numeric values
+        - the second through n-th rows contain strings where at least one value's
+          length differs from that of the putative header of that column.
+
+      Twenty rows after the first row are sampled; if more than half of columns +
+      rows meet the criteria, :const:`True` is returned.
+
+   .. note::
+
+      This method is a rough heuristic and may produce both false positives and
+      negatives.
 
 An example for :class:`Sniffer` use::
 
diff --git a/Lib/csv.py b/Lib/csv.py
index dc85077f3ec..bb3ee269ae7 100644
--- a/Lib/csv.py
+++ b/Lib/csv.py
@@ -409,14 +409,10 @@ def has_header(self, sample):
                 continue # skip rows that have irregular number of columns
 
             for col in list(columnTypes.keys()):
-
-                for thisType in [int, float, complex]:
-                    try:
-                        thisType(row[col])
-                        break
-                    except (ValueError, OverflowError):
-                        pass
-                else:
+                thisType = complex
+                try:
+                    thisType(row[col])
+                except (ValueError, OverflowError):
                     # fallback to length of string
                     thisType = len(row[col])
 
diff --git a/Lib/test/test_csv.py b/Lib/test/test_csv.py
index 18b86aa71a5..09e72a71f1d 100644
--- a/Lib/test/test_csv.py
+++ b/Lib/test/test_csv.py
@@ -1020,6 +1020,42 @@ class TestSniffer(unittest.TestCase):
 'Stonecutters ''Seafood'' and Chop House'+ 'Lemont'+ 'IL'+ '12/19/02'+ 'Week Back'
 """
 
+    sample10 = dedent("""
+                        abc,def
+                        ghijkl,mno
+                        ghi,jkl
+                        """)
+
+    sample11 = dedent("""
+                        abc,def
+                        ghijkl,mnop
+                        ghi,jkl
+                         """)
+
+    sample12 = dedent(""""time","forces"
+                        1,1.5
+                        0.5,5+0j
+                        0,0
+                        1+1j,6
+                        """)
+
+    sample13 = dedent(""""time","forces"
+                        0,0
+                        1,2
+                        a,b
+                        """)
+
+    def test_issue43625(self):
+        sniffer = csv.Sniffer()
+        self.assertTrue(sniffer.has_header(self.sample12))
+        self.assertFalse(sniffer.has_header(self.sample13))
+
+    def test_has_header_strings(self):
+        "More to document existing (unexpected?) behavior than anything else."
+        sniffer = csv.Sniffer()
+        self.assertFalse(sniffer.has_header(self.sample10))
+        self.assertFalse(sniffer.has_header(self.sample11))
+
     def test_has_header(self):
         sniffer = csv.Sniffer()
         self.assertIs(sniffer.has_header(self.sample1), False)
diff --git a/Misc/NEWS.d/next/Library/2021-06-29-07-27-08.bpo-43625.ZlAxhp.rst b/Misc/NEWS.d/next/Library/2021-06-29-07-27-08.bpo-43625.ZlAxhp.rst
new file mode 100644
index 00000000000..a21975b948e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-06-29-07-27-08.bpo-43625.ZlAxhp.rst
@@ -0,0 +1,2 @@
+Fix a bug in the detection of CSV file headers by
+:meth:`csv.Sniffer.has_header` and improve documentation of same.