diff --git a/.travis.yml b/.travis.yml
index 39c75af1e..beb09e309 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,6 +4,7 @@ services: docker
 env:
   - VERSION=3.7 VARIANT=stretch
   - VERSION=3.7 VARIANT=stretch/slim
+  - VERSION=3.7 VARIANT=alpine3.8
   - VERSION=3.7 VARIANT=alpine3.7
   - VERSION=3.6 VARIANT=stretch
   - VERSION=3.6 VARIANT=stretch/slim
diff --git a/3.7/alpine3.8/Dockerfile b/3.7/alpine3.8/Dockerfile
new file mode 100644
index 000000000..f53793fec
--- /dev/null
+++ b/3.7/alpine3.8/Dockerfile
@@ -0,0 +1,132 @@
+#
+# NOTE: THIS DOCKERFILE IS GENERATED VIA "update.sh"
+#
+# PLEASE DO NOT EDIT IT DIRECTLY.
+#
+
+FROM alpine:3.8
+
+# ensure local python is preferred over distribution python
+ENV PATH /usr/local/bin:$PATH
+
+# http://bugs.python.org/issue19846
+# > At the moment, setting "LANG=C" on a Linux system *fundamentally breaks Python 3*, and that's not OK.
+ENV LANG C.UTF-8
+
+# install ca-certificates so that HTTPS works consistently
+# the other runtime dependencies for Python are installed later
+RUN apk add --no-cache ca-certificates
+
+ENV GPG_KEY 0D96DF4D4110E5C43FBFB17F2D347EA6AA65421D
+ENV PYTHON_VERSION 3.7.0
+
+RUN set -ex \
+	&& apk add --no-cache --virtual .fetch-deps \
+		gnupg \
+		libressl \
+		tar \
+		xz \
+	\
+	&& wget -O python.tar.xz "https://www.python.org/ftp/python/${PYTHON_VERSION%%[a-z]*}/Python-$PYTHON_VERSION.tar.xz" \
+	&& wget -O python.tar.xz.asc "https://www.python.org/ftp/python/${PYTHON_VERSION%%[a-z]*}/Python-$PYTHON_VERSION.tar.xz.asc" \
+	&& export GNUPGHOME="$(mktemp -d)" \
+	&& gpg --keyserver ha.pool.sks-keyservers.net --recv-keys "$GPG_KEY" \
+	&& gpg --batch --verify python.tar.xz.asc python.tar.xz \
+	&& rm -rf "$GNUPGHOME" python.tar.xz.asc \
+	&& mkdir -p /usr/src/python \
+	&& tar -xJC /usr/src/python --strip-components=1 -f python.tar.xz \
+	&& rm python.tar.xz \
+	\
+	&& apk add --no-cache --virtual .build-deps  \
+		bzip2-dev \
+		coreutils \
+		dpkg-dev dpkg \
+		expat-dev \
+		gcc \
+		gdbm-dev \
+		libc-dev \
+		libffi-dev \
+		libnsl-dev \
+		libressl \
+		libressl-dev \
+		libtirpc-dev \
+		linux-headers \
+		make \
+		ncurses-dev \
+		pax-utils \
+		readline-dev \
+		sqlite-dev \
+		tcl-dev \
+		tk \
+		tk-dev \
+		xz-dev \
+		zlib-dev \
+# add build deps before removing fetch deps in case there's overlap
+	&& apk del .fetch-deps \
+	\
+	&& cd /usr/src/python \
+	&& gnuArch="$(dpkg-architecture --query DEB_BUILD_GNU_TYPE)" \
+	&& ./configure \
+		--build="$gnuArch" \
+		--enable-loadable-sqlite-extensions \
+		--enable-shared \
+		--with-system-expat \
+		--with-system-ffi \
+		--without-ensurepip \
+	&& make -j "$(nproc)" \
+# set thread stack size to 1MB so we don't segfault before we hit sys.getrecursionlimit()
+# https://github.com/alpinelinux/aports/commit/2026e1259422d4e0cf92391ca2d3844356c649d0
+		EXTRA_CFLAGS="-DTHREAD_STACK_SIZE=0x100000" \
+	&& make install \
+	\
+	&& runDeps="$( \
+		scanelf --needed --nobanner --format '%n#p' --recursive /usr/local \
+			| tr ',' '\n' \
+			| sort -u \
+			| awk 'system("[ -e /usr/local/lib/" $1 " ]") == 0 { next } { print "so:" $1 }' \
+	)" \
+	&& apk add --virtual .python-rundeps $runDeps \
+	&& apk del .build-deps \
+	\
+	&& find /usr/local -depth \
+		\( \
+			\( -type d -a \( -name test -o -name tests \) \) \
+			-o \
+			\( -type f -a \( -name '*.pyc' -o -name '*.pyo' \) \) \
+		\) -exec rm -rf '{}' + \
+	&& rm -rf /usr/src/python
+
+# make some useful symlinks that are expected to exist
+RUN cd /usr/local/bin \
+	&& ln -s idle3 idle \
+	&& ln -s pydoc3 pydoc \
+	&& ln -s python3 python \
+	&& ln -s python3-config python-config
+
+# if this is called "PIP_VERSION", pip explodes with "ValueError: invalid truth value '<VERSION>'"
+ENV PYTHON_PIP_VERSION 10.0.1
+
+RUN set -ex; \
+	\
+	apk add --no-cache --virtual .fetch-deps libressl; \
+	\
+	wget -O get-pip.py 'https://bootstrap.pypa.io/get-pip.py'; \
+	\
+	apk del .fetch-deps; \
+	\
+	python get-pip.py \
+		--disable-pip-version-check \
+		--no-cache-dir \
+		"pip==$PYTHON_PIP_VERSION" \
+	; \
+	pip --version; \
+	\
+	find /usr/local -depth \
+		\( \
+			\( -type d -a \( -name test -o -name tests \) \) \
+			-o \
+			\( -type f -a \( -name '*.pyc' -o -name '*.pyo' \) \) \
+		\) -exec rm -rf '{}' +; \
+	rm -f get-pip.py
+
+CMD ["python3"]
diff --git a/update.sh b/update.sh
index 11683d650..a80eee5bb 100755
--- a/update.sh
+++ b/update.sh
@@ -112,7 +112,7 @@ for version in "${versions[@]}"; do
 	echo "$version: $fullVersion"
 
 	for v in \
-		alpine{3.6,3.7} \
+		alpine{3.6,3.7,3.8} \
 		{wheezy,jessie,stretch}{/slim,/onbuild,} \
 		windows/nanoserver-{1709,sac2016} \
 		windows/windowsservercore-{1709,ltsc2016} \
@@ -154,8 +154,8 @@ for version in "${versions[@]}"; do
 		esac
 
 		# https://bugs.python.org/issue32598 (Python 3.7.0b1+)
-		# TL;DR: Python 3.7+ uses OpenSSL functionality which LibreSSL doesn't implement (yet?)
-		if [[ "$version" == 3.7* ]] && [[ "$variant" == alpine* ]]; then
+		# TL;DR: Python 3.7+ uses OpenSSL functionality which LibreSSL 2.6.x in Alpine 3.7 doesn't implement
+		if [[ "$version" == 3.7* ]] && [[ "$variant" == alpine3.7 ]]; then
 			sed -ri -e 's/libressl/openssl/g' "$dir/Dockerfile"
 		fi
 

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