diff --git a/Dockerfile b/Dockerfile
index 27e3831..e504e94 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -21,8 +21,18 @@ ENV TOOLCHAIN_ARCHS="i686 x86_64 armv7 aarch64"
 # Build everything and clean up, in one step
 COPY *.sh libssp-Makefile ./
 COPY wrappers/*.sh ./wrappers/
+COPY wrappers/*.c ./wrappers/
 RUN ./build-all.sh $TOOLCHAIN_PREFIX && \
     ./strip-llvm.sh $TOOLCHAIN_PREFIX && \
     rm -rf /build
 
+# Cheating: Pull strip and objcopy from the normal binutils package.
+RUN apt-get update -qq && \
+    apt-get install -qqy binutils-mingw-w64-x86-64 && \
+    cp /usr/bin/x86_64-w64-mingw32-strip $TOOLCHAIN_PREFIX/bin/binutils-strip && \
+    cp /usr/bin/x86_64-w64-mingw32-objcopy $TOOLCHAIN_PREFIX/bin/binutils-objcopy && \
+    apt-get remove -qqy binutils-mingw-w64-x86-64 && \
+    apt-get clean -y && \
+    rm -rf /var/lib/apt/lists/*
+
 ENV PATH=$TOOLCHAIN_PREFIX/bin:$PATH
diff --git a/Dockerfile.dev b/Dockerfile.dev
index 3e32d72..cdcc6d1 100644
--- a/Dockerfile.dev
+++ b/Dockerfile.dev
@@ -25,6 +25,7 @@ ENV TOOLCHAIN_ARCHS="i686 x86_64 armv7 aarch64"
 
 # Install the usual $TUPLE-clang binaries
 COPY wrappers/*.sh ./wrappers/
+COPY wrappers/*.c ./wrappers/
 COPY install-wrappers.sh .
 RUN ./install-wrappers.sh $TOOLCHAIN_PREFIX
 
@@ -72,3 +73,12 @@ RUN ./build-libssp.sh $TOOLCHAIN_PREFIX
 # size as long as it is in a separate RUN layer though.)
 COPY strip-llvm.sh .
 RUN ./strip-llvm.sh $TOOLCHAIN_PREFIX
+
+# Cheating: Pull strip and objcopy from the normal binutils package.
+RUN apt-get update -qq && \
+    apt-get install -qqy binutils-mingw-w64-x86-64 && \
+    cp /usr/bin/x86_64-w64-mingw32-strip $TOOLCHAIN_PREFIX/bin/binutils-strip && \
+    cp /usr/bin/x86_64-w64-mingw32-objcopy $TOOLCHAIN_PREFIX/bin/binutils-objcopy && \
+    apt-get remove -qqy binutils-mingw-w64-x86-64 && \
+    apt-get clean -y && \
+    rm -rf /var/lib/apt/lists/*
diff --git a/install-wrappers.sh b/install-wrappers.sh
index 08c53b2..22538e6 100755
--- a/install-wrappers.sh
+++ b/install-wrappers.sh
@@ -12,6 +12,7 @@ PREFIX="$1"
 
 mkdir -p $PREFIX/bin
 cp wrappers/*-wrapper.sh $PREFIX/bin
+cc wrappers/change-pe-arch.c -o $PREFIX/bin/change-pe-arch
 cd $PREFIX/bin
 for arch in $ARCHS; do
     for exec in clang clang++ gcc g++; do
@@ -20,10 +21,10 @@ for arch in $ARCHS; do
     for exec in ar ranlib nm strings; do
         ln -sf llvm-$exec $arch-w64-mingw32-$exec || true
     done
-    for exec in strip; do
-        ln -sf $(which true) $arch-w64-mingw32-$exec
-    done
     for exec in ld objdump windres dlltool; do
         ln -sf $exec-wrapper.sh $arch-w64-mingw32-$exec
     done
+    for exec in objcopy strip; do
+        ln -sf objcopy-wrapper.sh $arch-w64-mingw32-$exec
+    done
 done
diff --git a/wrappers/change-pe-arch.c b/wrappers/change-pe-arch.c
new file mode 100644
index 0000000..36562c8
--- /dev/null
+++ b/wrappers/change-pe-arch.c
@@ -0,0 +1,164 @@
+/*
+ * Copyright (c) 2018 Martin Storsjo
+ *
+ * This file is part of llvm-mingw.
+ *
+ * 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.
+ */
+
+#include <stdio.h>
+#include <stdint.h>
+#include <string.h>
+
+#define IMAGE_DOS_SIGNATURE 0x5A4D
+#define IMAGE_NT_SIGNATURE  0x00004550
+
+#define IMAGE_FILE_MACHINE_AMD64 0x8664
+#define IMAGE_FILE_MACHINE_ARMNT  0x1C4
+#define IMAGE_FILE_MACHINE_ARM64 0xAA64
+#define IMAGE_FILE_MACHINE_I386   0x14C
+
+static uint16_t readUint16(FILE *f) {
+    uint8_t buf[2];
+    if (fread(buf, 1, 2, f) != 2)
+        return -1;
+    return buf[0] | (buf[1] << 8);
+}
+
+static uint32_t readUint32(FILE *f) {
+    uint8_t buf[4];
+    if (fread(buf, 1, 4, f) != 4)
+        return -1;
+    return buf[0] | (buf[1] << 8) | (buf[2] << 16) | (buf[3] << 24);
+}
+
+static void writeUint16(FILE *f, uint16_t val) {
+    uint8_t buf[2];
+    buf[0] =  val       & 0xff;
+    buf[1] = (val >> 8) & 0xff;
+    if (fwrite(buf, 1, 2, f) != 2)
+        perror("fwrite");
+}
+
+static void writeUint32(FILE *f, uint32_t val) {
+    uint8_t buf[4];
+    buf[0] =  val        & 0xff;
+    buf[1] = (val >>  8) & 0xff;
+    buf[2] = (val >> 16) & 0xff;
+    buf[3] = (val >> 24) & 0xff;
+    if (fwrite(buf, 1, 4, f) != 4)
+        perror("fwrite");
+}
+
+static uint16_t archToInt(const char *str) {
+    if (!strcmp(str, "i686"))
+        return IMAGE_FILE_MACHINE_I386;
+    else if (!strcmp(str, "x86_64"))
+        return IMAGE_FILE_MACHINE_AMD64;
+    else if (!strcmp(str, "armv7"))
+        return IMAGE_FILE_MACHINE_ARMNT;
+    else if (!strcmp(str, "aarch64"))
+        return IMAGE_FILE_MACHINE_ARM64;
+    fprintf(stderr, "Unknown architecture %s\n", str);
+    return 0;
+}
+
+static int is64Bit(uint16_t arch) {
+    switch (arch) {
+    case IMAGE_FILE_MACHINE_AMD64:
+    case IMAGE_FILE_MACHINE_ARM64:
+        return 1;
+    default:
+        return 0;
+    }
+}
+
+void help(const char *argv0) {
+    printf("%s [-check] [-from arch] [-to arch] file\n", argv0);
+}
+
+int main(int argc, char *argv[]) {
+    int check = 0;
+    uint16_t from = 0, to = 0;
+    int i;
+    const char *filename = NULL;
+    FILE *f;
+    uint32_t offset;
+    for (i = 1; i < argc; i++) {
+        if (!strcmp(argv[i], "-check")) {
+            check = 1;
+        } else if (!strcmp(argv[i], "-from") && i + 1 < argc) {
+            from = archToInt(argv[++i]);
+        } else if (!strcmp(argv[i], "-to") && i + 1 < argc) {
+            to = archToInt(argv[++i]);
+        } else if (!filename) {
+            filename = argv[i];
+        } else {
+            help(argv[0]);
+            return 1;
+        }
+    }
+    if ((!check && (!from || !to)) || !filename) {
+        help(argv[0]);
+        return 1;
+    }
+    if (!check && is64Bit(from) != is64Bit(to)) {
+        fprintf(stderr, "Mismatched atchitecture bitness\n");
+        return 1;
+    }
+    f = fopen(filename, "r+b");
+    if (!f) {
+        perror(filename);
+        return 1;
+    }
+    if (readUint16(f) != IMAGE_DOS_SIGNATURE) {
+        if (!check)
+            fprintf(stderr, "Incorrect DOS header signature\n");
+        goto fail;
+    }
+    if (fseek(f, 0x3c, SEEK_SET) == -1) { // offsetof(IMAGE_DOS_HEADER, e_lfanew)
+        if (!check)
+            fprintf(stderr, "Unable to seek\n");
+        goto fail;
+    }
+    offset = readUint32(f);
+    if (fseek(f, offset, SEEK_SET) == -1) {
+        if (!check)
+            fprintf(stderr, "Unable to seek\n");
+        goto fail;
+    }
+    if (readUint32(f) != IMAGE_NT_SIGNATURE) {
+        if (!check)
+            fprintf(stderr, "Incorrect NT header signature\n");
+        goto fail;
+    }
+    if (check)
+        goto done;
+    if (readUint16(f) != from) {
+        fprintf(stderr, "Unexpected architecture\n");
+        goto fail;
+    }
+    fseek(f, -2, SEEK_CUR);
+    writeUint16(f, to);
+    if (fseek(f, offset + 0x58, SEEK_SET) == -1) { // offsetof(IMAGE_NT_HEADERS, OptionalHeader.CheckSum)
+        fprintf(stderr, "Unable to seek\n");
+        goto fail;
+    }
+    writeUint32(f, 0);
+done:
+    fclose(f);
+    return 0;
+fail:
+    fclose(f);
+    return 1;
+}
diff --git a/wrappers/objcopy-wrapper.sh b/wrappers/objcopy-wrapper.sh
new file mode 100755
index 0000000..8e6ef64
--- /dev/null
+++ b/wrappers/objcopy-wrapper.sh
@@ -0,0 +1,90 @@
+#!/bin/sh
+
+set -e
+
+DIR="$(cd "$(dirname "$0")" && pwd)"
+TARGET="$(basename $0 | sed 's/-[^-]*$//')"
+EXE=$(basename $0 | sed 's/.*-\([^-]*\)/\1/')
+ARCH=$(echo $TARGET | sed 's/-.*//')
+
+IN=""
+OUT=""
+ARGS=""
+STRIP=""
+while [ $# -gt 0 ]; do
+    case $1 in
+    --strip*|-g|-S)
+        STRIP=1
+        ;;
+    -*)
+        ;;
+    *)
+        if [ -z "$IN" ]; then
+            IN="$1"
+        elif [ -z "$OUT" ]; then
+            OUT="$1"
+        else
+            echo Unhandled arg $1
+            exit 1
+        fi
+        ;;
+    esac
+    ARGS="$ARGS $1"
+    shift
+done
+if [ -n "$IN" ] && [ -z "$OUT" ]; then
+	OUT="$IN"
+fi
+
+case $ARCH in
+i686|x86_64) COMPAT_ARCH=$ARCH;;
+armv7)       COMPAT_ARCH=i686;;
+aarch64)     COMPAT_ARCH=x86_64;;
+esac
+
+convert() {
+    if [ "$ARCH" = "$COMPAT_ARCH" ]; then
+        return
+    fi
+    $DIR/change-pe-arch "$@"
+}
+
+checkstrip() {
+    if [ "$EXE" = "strip" ]; then
+        return 0
+    elif [ -n "$STRIP" ]; then
+        if [ "$IN" != "$OUT" ]; then
+            cp "$IN" "$OUT"
+        fi
+        return 0
+    else
+        return 1
+    fi
+}
+
+if [ "$ARCH" != "$COMPAT_ARCH" ] && ! $DIR/change-pe-arch -check "$IN"; then
+    if checkstrip; then
+        echo Ignoring strip of non-executable \(object file\?\) >&2
+        exit 0
+    else
+        echo Unsupported "$0 $ARGS", not supported for non-executable \(object file\?\) >&2
+        exit 1
+    fi
+fi
+
+if [ -x $DIR/binutils-$EXE ]; then
+    convert -from $ARCH -to $COMPAT_ARCH "$IN"
+    $DIR/binutils-$EXE $ARGS
+    convert -from $COMPAT_ARCH -to $ARCH "$OUT"
+    if [ "$OUT" != "$IN" ]; then
+        convert -from $COMPAT_ARCH -to $ARCH "$IN"
+    fi
+else
+    if checkstrip; then
+        echo Ignoring strip, missing binutils-$EXE >&2
+        exit 0
+    else
+        echo Unsupported "$0 $ARGS", missing binutils-$EXE >&2
+        exit 1
+    fi
+fi