diff --git a/doc/api/zlib.md b/doc/api/zlib.md
index fa1f39e72e4cde..98501507084aaa 100644
--- a/doc/api/zlib.md
+++ b/doc/api/zlib.md
@@ -258,8 +258,7 @@ All of the constants defined in `zlib.h` are also defined on
 `require('zlib').constants`. In the normal course of operations, it will not be
 necessary to use these constants. They are documented so that their presence is
 not surprising. This section is taken almost directly from the
-[zlib documentation][]. See <https://zlib.net/manual.html#Constants> for more
-details.
+[zlib documentation][].
 
 Previously, the constants were available directly from `require('zlib')`, for
 instance `zlib.Z_NO_FLUSH`. Accessing the constants directly from the module is
@@ -408,8 +407,8 @@ ignored by the decompression classes.
   empty dictionary by default)
 * `info` {boolean} (If `true`, returns an object with `buffer` and `engine`.)
 
-See the description of `deflateInit2` and `inflateInit2` at
-<https://zlib.net/manual.html#Advanced> for more information on these.
+See the [`deflateInit2` and `inflateInit2`][] documentation for more
+information.
 
 ## Class: BrotliOptions
 <!-- YAML
@@ -1039,6 +1038,7 @@ Decompress a chunk of data with [`Unzip`][].
 [`Inflate`]: #zlib_class_zlib_inflate
 [`TypedArray`]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
 [`Unzip`]: #zlib_class_zlib_unzip
+[`deflateInit2` and `inflateInit2`]: https://zlib.net/manual.html#Advanced
 [`stream.Transform`]: stream.html#stream_class_stream_transform
 [`zlib.bytesWritten`]: #zlib_zlib_byteswritten
 [Brotli parameters]: #zlib_brotli_constants