diff --git a/README.md b/README.md
index 279cf8a5..78b13516 100644
--- a/README.md
+++ b/README.md
@@ -675,7 +675,6 @@ name | default | description
 `PYENV_DEBUG` | | Outputs debug information.<br>Also as: `pyenv --debug <subcommand>`
 `PYENV_HOOK_PATH` | [_see wiki_][hooks] | Colon-separated list of paths searched for pyenv hooks.
 `PYENV_DIR` | `$PWD` | Directory to start searching for `.python-version` files.
-`PYTHON_BUILD_ARIA2_OPTS` | | Used to pass additional parameters to [`aria2`](https://aria2.github.io/).<br>If the `aria2c` binary is available on `PATH`, pyenv uses `aria2c` instead of `curl` or `wget` to download the Python Source code. If you have an unstable internet connection, you can use this variable to instruct `aria2` to accelerate the download.<br>In most cases, you will only need to use `-x 10 -k 1M` as value to `PYTHON_BUILD_ARIA2_OPTS` environment variable
 
 See also [_Special environment variables_ in Python-Build's README](plugins/python-build/README.md#special-environment-variables)
 for environment variables that can be used to customize the build.
diff --git a/plugins/python-build/README.md b/plugins/python-build/README.md
index 7fd92165..83f48882 100644
--- a/plugins/python-build/README.md
+++ b/plugins/python-build/README.md
@@ -157,6 +157,7 @@ You can set certain environment variables to control the build process.
 * `PYTHON_BUILD_SKIP_MIRROR`, if set, forces python-build to download packages from
   their original source URLs instead of using a mirror.
 * `PYTHON_BUILD_HTTP_CLIENT`, explicitly specify the HTTP client type to use. `aria2`, `curl` and `wget` are the supported values and by default, are searched in that order.
+* `PYTHON_BUILD_CURL_OPTS`, `PYTHON_BUILD_WGET_OPTS`, `PYTHON_BUILD_ARIA2_OPTS` pass additional parameters to the corresponding HTTP client.
 * `PYTHON_BUILD_SKIP_HOMEBREW`, if set, will not search for libraries installed by Homebrew when it would normally will.
 * `PYTHON_BUILD_USE_HOMEBREW`, if set, will search for libraries installed by Homebrew when it would normally not.
 * `PYTHON_BUILD_HOMEBREW_OPENSSL_FORMULA`, override the Homebrew OpenSSL formula to use.