diff --git a/Makefile b/Makefile
index 10624ed5..097e5f16 100644
--- a/Makefile
+++ b/Makefile
@@ -1,7 +1,11 @@
 MAKEFLAGS := --jobs=1
+
 VERSION := $(shell git describe --tag)
 COMMIT := $(shell git rev-parse --short HEAD)
 
+PY_BIN := $(shell tools/get-python-bin.sh python)
+PIP_BIN := $(shell tools/get-python-bin.sh pip)
+
 .PHONY:
 
 help:
@@ -111,25 +115,13 @@ build-deps-ubuntu:
 docs: docs-deps docs-build
 
 docs-build: .PHONY
-	@if ! /bin/echo -e "import sys\nif sys.version_info < (3,8):\n exit(1)" | python3; then \
-	  if which python3.8; then \
-	  	echo "python3.8 $(shell which mkdocs) build"; \
-	    python3.8 $(shell which mkdocs) build; \
-	  else \
-	    echo "ERROR: Python version too low. mkdocs-material needs >= 3.8"; \
-	    exit 1; \
-	  fi; \
-	else \
-	  echo "mkdocs build"; \
-	  mkdocs build; \
-	fi
+	PY=$$(which $(PY_BIN)) && MKDOCS=$$(which mkdocs) && $$PY $$MKDOCS build
 
 docs-deps: .PHONY
-	pip3 install -r requirements.txt
+	PIP=$$(which $(PIP_BIN)) && $$PIP install -r requirements.txt
 
 docs-deps-update: .PHONY
-	pip3 install -r requirements.txt --upgrade
-
+	PIP=$$(which $(PIP_BIN)) && $$PIP install -r requirements.txt --upgrade
 
 # Web app
 
diff --git a/tools/get-python-bin.sh b/tools/get-python-bin.sh
new file mode 100755
index 00000000..8c0eb857
--- /dev/null
+++ b/tools/get-python-bin.sh
@@ -0,0 +1,46 @@
+#!/usr/bin/env bash
+
+# Synopsis:
+# - get-python-bin.sh python
+# - get-python-bin.sh pip
+#
+# This script selects the most suitable `python` / `pip` binary available
+# for building docs that's installed in this system.
+#
+# If no usable version of Python is available, this script will exit with a
+# non-zero code.
+
+set -e
+
+case "$1" in
+    "python" | "pip")
+        BIN_PREFIX="$1"
+        ;;
+    *)
+        echo "Incorrect usage" >&2
+        exit 1
+        ;;
+esac
+
+# if `python3` is >= 3.8 and `pip3` is available, use that
+if echo -e "import sys\nif sys.version_info < (3,8):\n exit(1)" | python3 && \
+which pip3 1>/dev/null 2>&1; then
+    echo "${BIN_PREFIX}3"
+    exit 0
+fi
+
+# list all available `python3.N`, then use the newest that passes checks
+# compgen is bash-specific, but we asked for bash in shebang so it's fine
+MINOR_VERSION_CANDIDATES=$(compgen -c | grep -P '^python3\.[0-9]+$' | sed 's/python3\.//' | awk 'int($NF) >= 8' | sort -nr)
+for MINOR in ${MINOR_VERSION_CANDIDATES[@]}; do
+    # if both `python3.N` and `pip3.N` are available, use that
+    if which "python3.${MINOR}" 1>/dev/null 2>&1 && \
+    which "pip3.${MINOR}" 1>/dev/null 2>&1; then
+        echo "${BIN_PREFIX}3.${MINOR}"
+        exit 0
+    fi
+done
+
+# none found
+echo "No suitable version of Python found" >&2
+exit 2