diff --git a/pypdf/generic/_data_structures.py b/pypdf/generic/_data_structures.py
index 91f59f746..3ed891a00 100644
--- a/pypdf/generic/_data_structures.py
+++ b/pypdf/generic/_data_structures.py
@@ -828,16 +828,29 @@ def flate_encode(self) -> "EncodedStreamObject":
         if SA.FILTER in self:
             f = self[SA.FILTER]
             if isinstance(f, ArrayObject):
-                f.insert(0, NameObject(FT.FLATE_DECODE))
+                f = ArrayObject([NameObject(FT.FLATE_DECODE), *f])
+                try:
+                    parms = ArrayObject(
+                        [NullObject(), *self.get(SA.DECODE_PARMS, ArrayObject())]
+                    )
+                except TypeError:
+                    # case of error where the * operator is not working (not an array
+                    parms = ArrayObject(
+                        [NullObject(), self.get(SA.DECODE_PARMS, ArrayObject())]
+                    )
             else:
-                newf = ArrayObject()
-                newf.append(NameObject("/FlateDecode"))
-                newf.append(f)
-                f = newf
+                f = ArrayObject([NameObject(FT.FLATE_DECODE), f])
+                parms = ArrayObject(
+                    [NullObject(), self.get(SA.DECODE_PARMS, NullObject())]
+                )
         else:
-            f = NameObject("/FlateDecode")
+            f = NameObject(FT.FLATE_DECODE)
+            parms = None
         retval = EncodedStreamObject()
+        retval.update(self)
         retval[NameObject(SA.FILTER)] = f
+        if parms is not None:
+            retval[NameObject(SA.DECODE_PARMS)] = parms
         retval._data = FlateDecode.encode(self._data)
         return retval
 
@@ -894,7 +907,18 @@ def getData(self) -> Union[None, str, bytes]:  # deprecated
         return self.get_data()
 
     def set_data(self, data: Any) -> None:  # deprecated
-        raise PdfReadError("Creating EncodedStreamObject is not currently supported")
+        from ..filters import FlateDecode
+
+        if self.get(SA.FILTER, "") == FT.FLATE_DECODE:
+            if not isinstance(data, bytes):
+                raise TypeError("data must be bytes")
+            assert self.decoded_self is not None
+            self.decoded_self._data = data
+            self._data = FlateDecode.encode(data)
+        else:
+            raise PdfReadError(
+                "Streams encoded with different filter from only FlateDecode is not supported"
+            )
 
     def setData(self, data: Any) -> None:  # deprecated
         deprecation_with_replacement("setData", "set_data", "3.0.0")
diff --git a/tests/test_generic.py b/tests/test_generic.py
index 2302767f9..80f604f8b 100644
--- a/tests/test_generic.py
+++ b/tests/test_generic.py
@@ -1169,3 +1169,34 @@ def test_destination_withoutzoom():
     name = "2021_book_security.pdf"
     reader = PdfReader(BytesIO(get_pdf_from_url(url, name=name)))
     reader.outline
+
+
+def test_encodedstream_set_data():
+    """
+    EncodedStreamObject.set_data to extend data stream works.
+
+    Checks also the flate_encode.
+    """
+    pdf_path = RESOURCE_ROOT / "crazyones.pdf"
+    reader = PdfReader(pdf_path)
+    co = reader.pages[0]["/Contents"][0].get_object()
+    co.set_data(b"%hello\n" + co.get_data())
+    assert b"hello" in co.get_data()
+    b = BytesIO()
+    co.write_to_stream(b)
+    b.seek(0)
+    aa = read_object(b, None)
+    assert b"hello" in aa.get_data()
+    assert aa["/Filter"] == "/FlateDecode"
+    assert "/DecodeParms" not in aa
+    bb = aa.flate_encode()
+    assert b"hello" in bb.get_data()
+    assert bb["/Filter"] == ["/FlateDecode", "/FlateDecode"]
+    assert str(bb["/DecodeParms"]) == "[NullObject, NullObject]"
+    bb[NameObject("/Test")] = NameObject("/MyTest")
+    cc = bb.flate_encode()
+    assert bb["/Filter"] == ["/FlateDecode", "/FlateDecode"]
+    assert b"hello" in cc.get_data()
+    assert cc["/Filter"] == ["/FlateDecode", "/FlateDecode", "/FlateDecode"]
+    assert str(cc["/DecodeParms"]) == "[NullObject, NullObject, NullObject]"
+    assert cc[NameObject("/Test")] == "/MyTest"