diff --git a/Lib/bz2.py b/Lib/bz2.py
index ce07ebeb142d92..7447d12fc4b8c8 100644
--- a/Lib/bz2.py
+++ b/Lib/bz2.py
@@ -226,15 +226,23 @@ def write(self, data):
         """Write a byte string to the file.
 
         Returns the number of uncompressed bytes written, which is
-        always len(data). Note that due to buffering, the file on disk
-        may not reflect the data written until close() is called.
+        always the length of data in bytes. Note that due to buffering,
+        the file on disk may not reflect the data written until close()
+        is called.
         """
         with self._lock:
             self._check_can_write()
+            if isinstance(data, (bytes, bytearray)):
+                length = len(data)
+            else:
+                # accept any data that supports the buffer protocol
+                data = memoryview(data)
+                length = data.nbytes
+
             compressed = self._compressor.compress(data)
             self._fp.write(compressed)
-            self._pos += len(data)
-            return len(data)
+            self._pos += length
+            return length
 
     def writelines(self, seq):
         """Write a sequence of byte strings to the file.
diff --git a/Lib/lzma.py b/Lib/lzma.py
index 0817b872d2019f..0aa30fe87f8c0c 100644
--- a/Lib/lzma.py
+++ b/Lib/lzma.py
@@ -225,14 +225,22 @@ def write(self, data):
         """Write a bytes object to the file.
 
         Returns the number of uncompressed bytes written, which is
-        always len(data). Note that due to buffering, the file on disk
-        may not reflect the data written until close() is called.
+        always the length of data in bytes. Note that due to buffering,
+        the file on disk may not reflect the data written until close()
+        is called.
         """
         self._check_can_write()
+        if isinstance(data, (bytes, bytearray)):
+            length = len(data)
+        else:
+            # accept any data that supports the buffer protocol
+            data = memoryview(data)
+            length = data.nbytes
+
         compressed = self._compressor.compress(data)
         self._fp.write(compressed)
-        self._pos += len(data)
-        return len(data)
+        self._pos += length
+        return length
 
     def seek(self, offset, whence=io.SEEK_SET):
         """Change the file position.
diff --git a/Lib/test/test_bz2.py b/Lib/test/test_bz2.py
index 1fce9d82d25d6a..c84f70ebb094a6 100644
--- a/Lib/test/test_bz2.py
+++ b/Lib/test/test_bz2.py
@@ -1,6 +1,7 @@
 from test import support
 from test.support import bigmemtest, _4G
 
+import array
 import unittest
 from io import BytesIO, DEFAULT_BUFFER_SIZE
 import os
@@ -618,6 +619,14 @@ def test_read_truncated(self):
             with BZ2File(BytesIO(truncated[:i])) as f:
                 self.assertRaises(EOFError, f.read, 1)
 
+    def test_issue44439(self):
+        q = array.array('Q', [1, 2, 3, 4, 5])
+        LENGTH = len(q) * q.itemsize
+
+        with BZ2File(BytesIO(), 'w') as f:
+            self.assertEqual(f.write(q), LENGTH)
+            self.assertEqual(f.tell(), LENGTH)
+
 
 class BZ2CompressorTest(BaseTest):
     def testCompress(self):
diff --git a/Lib/test/test_lzma.py b/Lib/test/test_lzma.py
index 0f3af27efa909c..ef7dd6325d49f3 100644
--- a/Lib/test/test_lzma.py
+++ b/Lib/test/test_lzma.py
@@ -1,4 +1,5 @@
 import _compression
+import array
 from io import BytesIO, UnsupportedOperation, DEFAULT_BUFFER_SIZE
 import os
 import pathlib
@@ -1227,6 +1228,14 @@ def test_issue21872(self):
         self.assertTrue(d2.eof)
         self.assertEqual(out1 + out2, entire)
 
+    def test_issue44439(self):
+        q = array.array('Q', [1, 2, 3, 4, 5])
+        LENGTH = len(q) * q.itemsize
+
+        with LZMAFile(BytesIO(), 'w') as f:
+            self.assertEqual(f.write(q), LENGTH)
+            self.assertEqual(f.tell(), LENGTH)
+
 
 class OpenTestCase(unittest.TestCase):
 
diff --git a/Misc/NEWS.d/next/Library/2021-06-17-15-01-51.bpo-44439.1S7QhT.rst b/Misc/NEWS.d/next/Library/2021-06-17-15-01-51.bpo-44439.1S7QhT.rst
new file mode 100644
index 00000000000000..27396683700a83
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-06-17-15-01-51.bpo-44439.1S7QhT.rst
@@ -0,0 +1,3 @@
+Fix in :meth:`bz2.BZ2File.write` / :meth:`lzma.LZMAFile.write` methods, when
+the input data is an object that supports the buffer protocol, the file length
+may be wrong.