diff --git a/Buildscr b/Buildscr
index ba6ffca..69cc2d0 100644
--- a/Buildscr
+++ b/Buildscr
@@ -24,6 +24,16 @@ in puzzles do echo '$#define VER "Version $(Version)"' >> version.h
 # them!)
 in puzzles do perl -i -pe 's/Unidentified build/$(Version)/' osx/Info.plist
 
+ifneq "$(NOICONS)" yes then
+  # Run enough of a native Unix build to produce the various icons.
+  in . do cmake -B build-icons puzzles
+  in build-icons do make -j$(nproc) icons VERBOSE=1
+
+  # Copy the C icon files into the icons source subdirectory, for the
+  # distribution tarball.
+  in . do cp build-icons/icons/*-icon.c puzzles/icons
+endif
+
 # The very first thing we do is to make the source archive, before we
 # fill up the build directory with extra files.
 delegate -
@@ -38,13 +48,6 @@ delegate -
   return puzzles-$(Version).tar.gz
 enddelegate
 
-ifneq "$(NOICONS)" yes then
-  # Run enough of a native Unix build to produce the icons needed for
-  # the Windows builds and the website.
-  in puzzles do cmake -B build-icons .
-  in puzzles/build-icons do make -j$(nproc) icons VERBOSE=1
-endif
-
 ifneq "$(NOMACOS)" yes then
   # Build the OS X binaries and .dmg archive.
   delegate osx
@@ -59,8 +62,8 @@ ifneq "$(NOWINDOWS)" yes then
   in puzzles do make -f Makefile.doc clean
   in puzzles do make -f Makefile.doc -j$(nproc) # build help files for installer
 
-  in puzzles do cmake -B build-win64 -DCMAKE_BUILD_TYPE=Release -DCMAKE_MSVC_RUNTIME_LIBRARY=MultiThreaded -DCMAKE_TOOLCHAIN_FILE=$(cmake_toolchain_clangcl64) .
-  in puzzles do cmake -B build-win32 -DCMAKE_BUILD_TYPE=Release -DCMAKE_MSVC_RUNTIME_LIBRARY=MultiThreaded -DCMAKE_TOOLCHAIN_FILE=$(cmake_toolchain_clangcl32) .
+  in . with cmake_at_least_3.20 do cmake -B puzzles/build-win64 -DCMAKE_BUILD_TYPE=Release -DCMAKE_MSVC_RUNTIME_LIBRARY=MultiThreaded -DCMAKE_TOOLCHAIN_FILE=$(cmake_toolchain_clangcl64) -DICO_DIR=$$PWD/build-icons/icons puzzles
+  in . with cmake_at_least_3.20 do cmake -B puzzles/build-win32 -DCMAKE_BUILD_TYPE=Release -DCMAKE_MSVC_RUNTIME_LIBRARY=MultiThreaded -DCMAKE_TOOLCHAIN_FILE=$(cmake_toolchain_clangcl32) -DICO_DIR=$$PWD/build-icons/icons puzzles
   in puzzles/build-win64 do make -j$(nproc) VERBOSE=1
   in puzzles/build-win32 do make -j$(nproc) VERBOSE=1
 
@@ -150,7 +153,7 @@ in puzzles do echo RedirectMatch temp '(.*/)'puzzles-installer.msi '$$1'puzzles-
 
 # Phew, we're done. Deliver everything!
 ifneq "$(NOICONS)" yes then
-  deliver puzzles/build-icons/icons/*-web.png $@
+  deliver build-icons/icons/*-web.png $@
 endif
 ifneq "$(NOWINDOWS)" yes then
   deliver puzzles/winbin64/*.exe $@
diff --git a/cmake/platforms/unix.cmake b/cmake/platforms/unix.cmake
index 1bed675..b858be8 100644
--- a/cmake/platforms/unix.cmake
+++ b/cmake/platforms/unix.cmake
@@ -51,9 +51,21 @@ endif()
 
 function(get_platform_puzzle_extra_source_files OUTVAR NAME)
   if(build_icons AND EXISTS ${CMAKE_SOURCE_DIR}/icons/${NAME}.sav)
+    # If we have the equipment to rebuild the puzzles' icon images
+    # from scratch, do so. Then changes in the puzzle display code
+    # will cause the icon to auto-update.
     build_icon(${NAME})
     set(c_icon_file ${CMAKE_BINARY_DIR}/icons/${NAME}-icon.c)
+  elseif(EXISTS ${CMAKE_SOURCE_DIR}/icons/${NAME}-icon.c)
+    # Failing that, use a pre-built icon file in the 'icons'
+    # subdirectory, if there is one. (They don't exist in git, but the
+    # distribution tarball will have pre-built them and put them in
+    # there, so that users building from that can still have icons
+    # even if they don't have the wherewithal to rebuild them.)
+    set(c_icon_file ${CMAKE_SOURCE_DIR}/icons/${NAME}-icon.c)
   else()
+    # Failing even that, include no-icon.c to satisfy the link-time
+    # dependencies. The puzzles will build without nice icons.
     set(c_icon_file ${CMAKE_SOURCE_DIR}/no-icon.c)
   endif()
 
diff --git a/icons/icons.cmake b/icons/icons.cmake
index 873c3c7..b5ee02e 100644
--- a/icons/icons.cmake
+++ b/icons/icons.cmake
@@ -236,6 +236,7 @@ function(build_icon name)
     DEPENDS
       ${icon_srcdir}/cicon.pl
       ${cicon_pl_infiles})
+  list(APPEND output_icon_files ${icon_bindir}/${name}-icon.c)
 
   add_custom_target(${name}-icons DEPENDS ${output_icon_files})
   add_dependencies(icons ${name}-icons)