diff --git a/3.7/alpine3.7/Dockerfile b/3.7/alpine3.7/Dockerfile
index cb88aa2ab..89bb5c589 100644
--- a/3.7/alpine3.7/Dockerfile
+++ b/3.7/alpine3.7/Dockerfile
@@ -59,6 +59,7 @@ RUN set -ex \
 		tcl-dev \
 		tk \
 		tk-dev \
+		util-linux-dev \
 		xz-dev \
 		zlib-dev \
 # add build deps before removing fetch deps in case there's overlap
diff --git a/3.7/alpine3.8/Dockerfile b/3.7/alpine3.8/Dockerfile
index 9f57c79da..d84625e08 100644
--- a/3.7/alpine3.8/Dockerfile
+++ b/3.7/alpine3.8/Dockerfile
@@ -59,6 +59,7 @@ RUN set -ex \
 		tcl-dev \
 		tk \
 		tk-dev \
+		util-linux-dev \
 		xz-dev \
 		zlib-dev \
 # add build deps before removing fetch deps in case there's overlap
diff --git a/3.7/stretch/Dockerfile b/3.7/stretch/Dockerfile
index c2bef6ff7..a85354dcb 100644
--- a/3.7/stretch/Dockerfile
+++ b/3.7/stretch/Dockerfile
@@ -16,6 +16,7 @@ ENV LANG C.UTF-8
 # extra dependencies (over what buildpack-deps already includes)
 RUN apt-get update && apt-get install -y --no-install-recommends \
 		tk-dev \
+		uuid-dev \
 	&& rm -rf /var/lib/apt/lists/*
 
 ENV GPG_KEY 0D96DF4D4110E5C43FBFB17F2D347EA6AA65421D
diff --git a/3.7/stretch/slim/Dockerfile b/3.7/stretch/slim/Dockerfile
index c291b1beb..4ab40c8c3 100644
--- a/3.7/stretch/slim/Dockerfile
+++ b/3.7/stretch/slim/Dockerfile
@@ -40,6 +40,7 @@ RUN set -ex \
 		libssl-dev \
 		make \
 		tk-dev \
+		uuid-dev \
 		wget \
 		xz-utils \
 		zlib1g-dev \
diff --git a/Dockerfile-alpine.template b/Dockerfile-alpine.template
index 13ab1f95b..ad0dcdfa1 100644
--- a/Dockerfile-alpine.template
+++ b/Dockerfile-alpine.template
@@ -55,6 +55,7 @@ RUN set -ex \
 		tcl-dev \
 		tk \
 		tk-dev \
+		util-linux-dev \
 		xz-dev \
 		zlib-dev \
 # add build deps before removing fetch deps in case there's overlap
diff --git a/Dockerfile-debian.template b/Dockerfile-debian.template
index 293ec8acc..59ebcb955 100644
--- a/Dockerfile-debian.template
+++ b/Dockerfile-debian.template
@@ -12,6 +12,7 @@ RUN apt-get update && apt-get install -y --no-install-recommends \
 # Python 3.4 on Stretch+ needs to use an older version of "libssl-dev" (these lines both get removed for every other combination)
 		libssl-dev \
 		tk-dev \
+		uuid-dev \
 	&& rm -rf /var/lib/apt/lists/*
 
 ENV GPG_KEY %%PLACEHOLDER%%
diff --git a/Dockerfile-slim.template b/Dockerfile-slim.template
index 5257b3feb..a1fe875be 100644
--- a/Dockerfile-slim.template
+++ b/Dockerfile-slim.template
@@ -34,6 +34,7 @@ RUN set -ex \
 		libssl-dev \
 		make \
 		tk-dev \
+		uuid-dev \
 		wget \
 		xz-utils \
 		zlib1g-dev \
diff --git a/update.sh b/update.sh
index ba19bde89..f68c4e3b1 100755
--- a/update.sh
+++ b/update.sh
@@ -174,9 +174,18 @@ for version in "${versions[@]}"; do
 				;;& # (3.5*/alpine* needs to match the next block too)
 			# Libraries to build the nis module only available in Alpine 3.7+.
 			# Also require this patch https://bugs.python.org/issue32521 only available in Python 2.7, 3.6+.
-			3.4*/alpine* | 3.5*/alpine* | */alpine3.6)
+			3.[4-5]*/alpine* | */alpine3.6)
 				sed -ri -e '/libnsl-dev/d' -e '/libtirpc-dev/d' "$dir/Dockerfile"
+				;;& # (3.4*/alpine* and 3.5*/alpine* need to match the next block too)
+			# https://bugs.python.org/issue11063, https://bugs.python.org/issue20519 (Python 3.7.0+)
+			# A new native _uuid module improves uuid import time and avoids using ctypes.
+			# This requires the development libuuid headers.
+			3.[4-6]*/alpine*)
+				sed -ri -e '/util-linux-dev/d' "$dir/Dockerfile"
 				;;
+			3.[4-6]*)
+				sed -ri -e '/uuid-dev/d' "$dir/Dockerfile"
+				;;& # (other Debian variants need to match later blocks)
 			3.4/stretch*)
 				sed -ri -e 's/libssl-dev/libssl1.0-dev/g' "$dir/Dockerfile"
 				;;