diff --git a/Dockerfile b/Dockerfile
index d8932b11..4ca16edb 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -239,7 +239,7 @@ RUN mkdir nsis \
 
 FROM dl-cross AS variant-x64
 ENV ARCH=x86_64-w64-mingw32 \
-    GCC_ARCH_FLAG=--with-arch-32=pentium4 \
+    GCC_ARCH_FLAG="--with-arch-32=pentium4 --with-fpmath=sse" \
     GCC_MULTILIB=enable \
     CRT_LIB32=enable \
     CRT_LIB64=enable \
@@ -254,7 +254,7 @@ ENV ARCH=x86_64-w64-mingw32 \
 
 FROM dl-cross AS variant-x86
 ENV ARCH=i686-w64-mingw32 \
-    GCC_ARCH_FLAG=--with-arch=pentium4 \
+    GCC_ARCH_FLAG="--with-arch=pentium4 --with-fpmath=sse" \
     GCC_MULTILIB=disable \
     CRT_LIB32=enable \
     CRT_LIB64=disable \
diff --git a/README.md b/README.md
index ab3919c2..a767446a 100644
--- a/README.md
+++ b/README.md
@@ -85,10 +85,11 @@ toolchain targets Windows 7 by default.
 
 The x86 kit requires Windows XP or later and an SSE2-capable processor
 (e.g. at least Pentium 4); limited Unicode support. The toolchain targets
-the same by default. Runtimes contain SSE2 instructions, so GCC `-march`
-will not reliably target less capable processors when runtimes are linked
-(exceptions: `-lmemory`, `-lchkstk`). CMake, Ninja, and CCache require at
-least Windows 7.
+the same by default, with floating point math in SSE2 rather than x87
+(`-mfpmath=sse`), as on x64. Runtimes contain SSE2 instructions, so GCC
+`-march` will not reliably target less capable processors when runtimes
+are linked (exceptions: `-lmemory`, `-lchkstk`). CMake, Ninja, and
+CCache require at least Windows 7.
 
 ## Build cache