diff --git a/README.md b/README.md
index 563e145..ec28193 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,4 @@
-# emacs-build v0.3
+# emacs-build v0.3.1
 
 Scripts to build a distribution of Emacs from sources, using MSYS2 and Mingw64(32)
 
@@ -155,3 +155,7 @@ Regarding the extensions to Emacs and third-party utilities:
 - Emacs ships with a `site-start.el` that activates the directories for MSYS2 extensions.
 - Only one branch of Emacs can be built.
 - emacs-build no longer uses log files.
+
+## v0.3.1
+
+- Emacs-build upgrades GNU TLS version to at least 3.7.0, to allow safe https to MELPA.
diff --git a/emacs-build.sh b/emacs-build.sh
index 02e10d0..36fce39 100644
--- a/emacs-build.sh
+++ b/emacs-build.sh
@@ -33,6 +33,7 @@
 . scripts/hunspell.sh
 . scripts/gzip.sh
 . scripts/msys2_extra.sh
+. scripts/gnutls.sh
 
 function write_help () {
     cat "$emacs_build_root/scripts/help.txt"
@@ -190,15 +191,15 @@ function action2_install ()
         # HACK!!! Somehow libgmp is not installed as part of the
         # standalone Emacs build process. This is weird, but means
         # we have to copy it by hand.
-        make -j 4 -C $emacs_build_dir install \
+        make -j $emacs_build_threads -C $emacs_build_dir install \
             && cp "${mingw_dir}bin/libgmp"*.dll "$emacs_install_dir/bin/" \
+            && action2_patch_gnutls \
             && rm -f "$emacs_install_dir/bin/emacs-"*.exe \
             && find "$emacs_install_dir" -name '*.exe' -exec strip -g --strip-unneeded -X '{}' '+' \
             && cp "$emacs_build_root/scripts/site-start.el" "$emacs_install_dir/share/emacs/site-lisp" \
             && mkdir -p "$emacs_install_dir/usr/share/emacs/site-lisp/" \
             && cp "$emacs_install_dir/share/emacs/site-lisp/subdirs.el" \
                   "$emacs_install_dir/usr/share/emacs/site-lisp/subdirs.el"
-        dir "${emacs_install_dir}/bin"
     fi
 }
 
@@ -363,11 +364,13 @@ actions=""
 do_clean=""
 debug_dependency_list="false"
 emacs_compress_files=no
-emacs_build_version=0.3
+emacs_build_version=0.3.1
 emacs_slim_build=yes
 emacs_nativecomp=no
+emacs_build_threads=1
 while test -n "$*"; do
     case $1 in
+        --threads) shift; emacs_build_threads="$1";;
         --branch) shift; emacs_branch="$1";;
         --without-*) delete_feature `echo $1 | sed -e 's,--without-,,'`;;
         --with-*) add_feature `echo $1 | sed -e 's,--without-,,'`;;
@@ -425,7 +428,6 @@ if test -z "$actions"; then
     actions="action0_clone action1_ensure_packages action2_build action3_package_deps action5_package_all"
 fi
 features=`for f in $features; do echo $f; done | sort | uniq`
-echo $features
 
 # This is needed for pacman to return the right text
 export LANG=C
diff --git a/scripts/gnutls.sh b/scripts/gnutls.sh
new file mode 100644
index 0000000..a4fa568
--- /dev/null
+++ b/scripts/gnutls.sh
@@ -0,0 +1,36 @@
+#
+# GNU TLS library below 3.7.0 has problems connecting to MELPA
+# via https secure connections. This file downloads a more recent
+# version of the library.
+#
+
+function action2_patch_gnutls ()
+{
+    #
+    # If gnutls is not used or has a recent version, return
+    if [[ ! "$features" =~ .*gnutls.* ]]; then
+        return 0
+    fi
+    tls_version=`pacman -Qi mingw-w64-${mingw_prefix}-gnutls | grep Version | sed 's,Version[ ]*:[ ]*\([^ ]*\)$,\1,'`
+    if [[ ! "$tls_version" < "3.7.0" ]]; then
+        return 0
+    fi
+    echo Patching gnutls library because version ${tls_version} is too old.
+    #
+    # Download the official gnutls distribution and replace the
+    # existing libraries with this one. We assume this can be done
+    # because gnutls from mingw pulled the right dependencies
+    if test "$architecture" = "i686"; then
+        gnutls_link="https://gitlab.com/gnutls/gnutls/builds/artifacts/3.7.0/download?job=MinGW32.DLLs"
+        gnutls_dir="win32-build"
+    else
+        gnutls_link="https://gitlab.com/gnutls/gnutls/builds/artifacts/3.7.0/download?job=MinGW64.DLLs"
+        gnutls_dir="win64-build"
+    fi
+    (cd "$emacs_install_dir/" \
+         && rm -rf "$gnutls_dir" gnutls.zip \
+         && curl -L "$gnutls_link" > gnutls.zip \
+         && unzip -x gnutls.zip \
+         && mv "$gnutls_dir/bin/"* bin/ \
+         && rm -rf "$gnutls_dir" gnutls.zip)
+}