diff --git a/requirements.txt b/requirements.txt
index e060ed1a0..64ab24db3 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,4 +1,7 @@
-brotli==0.5.2
+# we use the official Brotli module on CPython and the CFFI-based
+# extension 'brotlipy' on PyPy
+brotli==0.6.0; platform_python_implementation != "PyPy"
+brotlipy==0.7.0; platform_python_implementation == "PyPy"
 unicodedata2==9.0.0.post4; python_version < '3.6' and platform_python_implementation != "PyPy"
 # TODO(anthrotype): update munkres to 1.0.9 once available:
 # https://github.com/bmc/munkres/issues/21