diff --git a/hack/make/build-deb b/hack/make/build-deb
index 2e7d2de402..102d5351d2 100644
--- a/hack/make/build-deb
+++ b/hack/make/build-deb
@@ -86,6 +86,16 @@ set -e
 		cat >> "$DEST/$version/Dockerfile.build" <<-EOF
 			RUN cp -aL hack/make/.build-deb debian
 			RUN { echo '$debSource (${debVersion}-0~${suite}) $suite; urgency=low'; echo; echo '  * Version: $VERSION'; echo; echo " -- $debMaintainer  $debDate"; } > debian/changelog && cat >&2 debian/changelog
+		EOF
+		# Remove the following case-based substitution when none of these are supported, and the TasksMax value is uncommented in docker.service
+		case "$version" in
+		debian-jessie|debian-wheezy|ubuntu-precise|ubuntu-trusty|ubuntu-wily)
+			;;
+		*)
+			echo "RUN sed -i -- 's/#TasksMax=infinity/TasksMax=infinity/' contrib/init/systemd/docker.service" >> "$DEST/$version/Dockerfile.build"
+			;;
+		esac
+		cat >> "$DEST/$version/Dockerfile.build" <<-EOF
 			RUN dpkg-buildpackage -uc -us
 		EOF
 		tempImage="docker-temp/build-deb:$version"