diff --git a/Makefile b/Makefile
index 77b5c5a3..548c23ee 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:
@@ -96,16 +100,13 @@ build-deps-ubuntu:
 docs: docs-deps docs-build
 
 docs-build: .PHONY
-	PY=$$(tools/get-python-bin.sh python) && MKDOCS=$$(which mkdocs) && \
-	$$PY $$MKDOCS build
+	PY=$$(which $(PY_BIN)) && MKDOCS=$$(which mkdocs) && $$PY $$MKDOCS build
 
 docs-deps: .PHONY
-	PIP=$$(tools/get-python-bin.sh pip) && \
-	$$PIP install -r requirements.txt
+	PIP=$$(which $(PIP_BIN)) && $$PIP install -r requirements.txt
 
 docs-deps-update: .PHONY
-	PIP=$$(tools/get-python-bin.sh pip) && \
-	$$PIP 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
index 13cce1e0..8c0eb857 100755
--- a/tools/get-python-bin.sh
+++ b/tools/get-python-bin.sh
@@ -29,13 +29,14 @@ which pip3 1>/dev/null 2>&1; then
     exit 0
 fi
 
-# check `python3.N` from newest to oldest
-CANDIDATE_SUFFIXES=("3.11" "3.10" "3.9" "3.8")
-for SUFFIX in ${CANDIDATE_SUFFIXES[@]}; do
+# list all available `python3.N`, then use the newest that passes checks
+# compgen is bash-specific, but we asked for bash in shebang so it's fine
+MINOR_VERSION_CANDIDATES=$(compgen -c | grep -P '^python3\.[0-9]+$' | sed 's/python3\.//' | awk 'int($NF) >= 8' | sort -nr)
+for MINOR in ${MINOR_VERSION_CANDIDATES[@]}; do
     # if both `python3.N` and `pip3.N` are available, use that
-    if which "python$SUFFIX" 1>/dev/null 2>&1 && \
-    which "pip$SUFFIX" 1>/dev/null 2>&1; then
-        echo "${BIN_PREFIX}${SUFFIX}"
+    if which "python3.${MINOR}" 1>/dev/null 2>&1 && \
+    which "pip3.${MINOR}" 1>/dev/null 2>&1; then
+        echo "${BIN_PREFIX}3.${MINOR}"
         exit 0
     fi
 done