diff --git a/.travis.yml b/.travis.yml
index 74f6705cb..4c1c817d0 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -7,9 +7,11 @@ env:
   - VERSION=3.6 VARIANT=jessie/slim
   - VERSION=3.6 VARIANT=alpine3.6
   - VERSION=3.6 VARIANT=alpine3.4
+  - VERSION=3.5 VARIANT=stretch
   - VERSION=3.5 VARIANT=jessie
   - VERSION=3.5 VARIANT=jessie/slim
   - VERSION=3.5 VARIANT=alpine3.4
+  - VERSION=3.4 VARIANT=stretch
   - VERSION=3.4 VARIANT=jessie
   - VERSION=3.4 VARIANT=jessie/slim
   - VERSION=3.4 VARIANT=wheezy
diff --git a/3.4/stretch/Dockerfile b/3.4/stretch/Dockerfile
new file mode 100644
index 000000000..bada4b934
--- /dev/null
+++ b/3.4/stretch/Dockerfile
@@ -0,0 +1,95 @@
+#
+# NOTE: THIS DOCKERFILE IS GENERATED VIA "update.sh"
+#
+# PLEASE DO NOT EDIT IT DIRECTLY.
+#
+
+FROM buildpack-deps:stretch
+
+# 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
+
+# runtime dependencies
+RUN apt-get update && apt-get install -y --no-install-recommends \
+		tcl \
+		tk \
+	&& rm -rf /var/lib/apt/lists/*
+
+ENV GPG_KEY 97FC712E4C024BBEA48A61ED3A5CA953F73C700D
+ENV PYTHON_VERSION 3.4.6
+
+RUN set -ex \
+	&& buildDeps=' \
+		dpkg-dev \
+		tcl-dev \
+		tk-dev \
+	' \
+	&& apt-get update && apt-get install -y $buildDeps --no-install-recommends && rm -rf /var/lib/apt/lists/* \
+	\
+	&& wget -O python.tar.xz "https://www.python.org/ftp/python/${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 \
+	\
+	&& 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)" \
+	&& make install \
+	&& ldconfig \
+	\
+	&& apt-get purge -y --auto-remove $buildDeps \
+	\
+	&& 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 9.0.1
+
+RUN set -ex; \
+	\
+	wget -O get-pip.py 'https://bootstrap.pypa.io/get-pip.py'; \
+	\
+	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/3.5/stretch/Dockerfile b/3.5/stretch/Dockerfile
new file mode 100644
index 000000000..1bee97453
--- /dev/null
+++ b/3.5/stretch/Dockerfile
@@ -0,0 +1,95 @@
+#
+# NOTE: THIS DOCKERFILE IS GENERATED VIA "update.sh"
+#
+# PLEASE DO NOT EDIT IT DIRECTLY.
+#
+
+FROM buildpack-deps:stretch
+
+# 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
+
+# runtime dependencies
+RUN apt-get update && apt-get install -y --no-install-recommends \
+		tcl \
+		tk \
+	&& rm -rf /var/lib/apt/lists/*
+
+ENV GPG_KEY 97FC712E4C024BBEA48A61ED3A5CA953F73C700D
+ENV PYTHON_VERSION 3.5.3
+
+RUN set -ex \
+	&& buildDeps=' \
+		dpkg-dev \
+		tcl-dev \
+		tk-dev \
+	' \
+	&& apt-get update && apt-get install -y $buildDeps --no-install-recommends && rm -rf /var/lib/apt/lists/* \
+	\
+	&& wget -O python.tar.xz "https://www.python.org/ftp/python/${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 \
+	\
+	&& 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)" \
+	&& make install \
+	&& ldconfig \
+	\
+	&& apt-get purge -y --auto-remove $buildDeps \
+	\
+	&& 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 9.0.1
+
+RUN set -ex; \
+	\
+	wget -O get-pip.py 'https://bootstrap.pypa.io/get-pip.py'; \
+	\
+	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"]