diff --git a/Dockerfile b/Dockerfile
index 4c39a2c..28daee8 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -44,16 +44,6 @@ ARG TOOLCHAIN_ARCHS="i686 x86_64 armv7 aarch64"
 
 ARG DEFAULT_CRT=ucrt
 
-# Build UASM, for building openmp. In the future, llvm-ml should be able
-# to handle it, but it doesn't yet.
-RUN git clone https://github.com/Terraspace/UASM && \
-    cd UASM && \
-    git checkout 16a853bd6de807fe2c42569f8375a029684c0f22 && \
-    make -f gccLinux64.mak -j$(nproc) && \
-    mkdir -p $TOOLCHAIN_PREFIX/bin && \
-    cp GccUnixR/uasm $TOOLCHAIN_PREFIX/bin
-COPY wrappers/uasm-wrapper.sh $TOOLCHAIN_PREFIX/bin
-
 # Build everything that uses the llvm monorepo. We need to build the mingw runtime before the compiler-rt/libunwind/libcxxabi/libcxx runtimes.
 COPY build-llvm.sh strip-llvm.sh install-wrappers.sh build-mingw-w64.sh build-mingw-w64-tools.sh build-compiler-rt.sh build-mingw-w64-libraries.sh build-libcxx.sh build-openmp.sh ./
 COPY wrappers/*.sh wrappers/*.c wrappers/*.h ./wrappers/
diff --git a/Dockerfile.dev b/Dockerfile.dev
index fe384f4..a34aa3f 100644
--- a/Dockerfile.dev
+++ b/Dockerfile.dev
@@ -158,15 +158,6 @@ RUN cd test && \
         done; \
     done
 
-# Build UASM, for building openmp. In the future, llvm-ml should be able
-# to handle it, but it doesn't yet.
-RUN git clone https://github.com/Terraspace/UASM && \
-    cd UASM && \
-    git checkout 16a853bd6de807fe2c42569f8375a029684c0f22 && \
-    make -f gccLinux64.mak -j$(nproc) && \
-    mkdir -p $TOOLCHAIN_PREFIX/bin && \
-    cp GccUnixR/uasm $TOOLCHAIN_PREFIX/bin
-COPY wrappers/uasm-wrapper.sh $TOOLCHAIN_PREFIX/bin
 # Build OpenMP
 COPY build-openmp.sh ./
 RUN ./build-openmp.sh $TOOLCHAIN_PREFIX
diff --git a/build-all.sh b/build-all.sh
index 7ae55e7..c1ce818 100755
--- a/build-all.sh
+++ b/build-all.sh
@@ -38,3 +38,4 @@ done
 ./build-libcxx.sh $PREFIX
 ./build-compiler-rt.sh $PREFIX --build-sanitizers
 ./build-libssp.sh $PREFIX
+./build-openmp.sh $PREFIX
diff --git a/build-openmp.sh b/build-openmp.sh
index 3b6c394..f73515a 100755
--- a/build-openmp.sh
+++ b/build-openmp.sh
@@ -54,31 +54,13 @@ else
     BUILDCMD=make
 fi
 
-if [ ! -x "$(which uasm)" ]; then
-    echo Building the OpenMP runtime requires UASM
-    exit 1
-fi
-UASM=uasm
-case $(uname) in
-MINGW*|MSYS*)
-    # On windows, only building with ninja works; building with msys make
-    # ends up mangling the forward slashes in certain options to UASM.
-    ;;
-*)
-    # UASM for unix doesn't support options with forward slashes, which CMake
-    # produces in some places. And ninja on windows can't execute a
-    # shell script, so this has to be done only on unix.
-    UASM=uasm-wrapper.sh
-    ;;
-esac
-
 for arch in $ARCHS; do
     CMAKEFLAGS=""
     case $arch in
     i686)
         ;;
     x86_64)
-        CMAKEFLAGS="$CMAKEFLAGS -DLIBOMP_ASMFLAGS=-win64"
+        CMAKEFLAGS="$CMAKEFLAGS -DLIBOMP_ASMFLAGS=-m64"
         ;;
     *)
         # Not supported
@@ -97,7 +79,7 @@ for arch in $ARCHS; do
         -DCMAKE_C_COMPILER=$arch-w64-mingw32-clang \
         -DCMAKE_CXX_COMPILER=$arch-w64-mingw32-clang++ \
         -DCMAKE_RC_COMPILER=$arch-w64-mingw32-windres \
-        -DCMAKE_ASM_MASM_COMPILER=$UASM \
+        -DCMAKE_ASM_MASM_COMPILER=llvm-ml \
         -DCMAKE_CROSSCOMPILING=TRUE \
         -DCMAKE_SYSTEM_NAME=Windows \
         -DCMAKE_AR="$PREFIX/bin/llvm-ar" \
diff --git a/wrappers/uasm-wrapper.sh b/wrappers/uasm-wrapper.sh
deleted file mode 100755
index d69e8b5..0000000
--- a/wrappers/uasm-wrapper.sh
+++ /dev/null
@@ -1,29 +0,0 @@
-#!/bin/sh
-#
-# Copyright (c) 2020 Martin Storsjo
-#
-# Permission to use, copy, modify, and/or distribute this software for any
-# purpose with or without fee is hereby granted, provided that the above
-# copyright notice and this permission notice appear in all copies.
-#
-# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
-# WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
-# MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
-# ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
-# WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
-# ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
-# OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
-
-ARGS=""
-while [ $# -gt 0 ]; do
-    a="$1"
-    case $a in
-    /safeseh|/coff|/c|/Fo)
-        a="-${a#/}"
-        ;;
-    esac
-    ARGS="$ARGS $a"
-    shift
-done
-
-uasm $ARGS