diff --git a/CMakeLists.txt b/CMakeLists.txt
index 80183b05..f18161d9 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1317,12 +1317,38 @@ set_target_properties(liblzma PROPERTIES
     SOVERSION "${xz_VERSION_MAJOR}"
     VERSION "${xz_VERSION}"
 
-    # It's liblzma.so or liblzma.dll, not libliblzma.so or lzma.dll.
-    # Avoid the name lzma.dll because it would conflict with LZMA SDK.
-    PREFIX ""
-    IMPORT_PREFIX ""
+    # The name liblzma a mess because in many places "lib" is just a prefix
+    # and not part of the actual name. (Don't name a new library this way!)
+    # Cygwin uses "cyg", MSYS2 uses "msys-", and some platforms use no prefix.
+    # However, we want to avoid lzma.dll on Windows as that would conflict
+    # with LZMA SDK. liblzma has been liblzma.dll on Windows since the
+    # beginning so try to stick with it.
+    #
+    # Up to XZ Utils 5.6.2 we set PREFIX and IMPORT_PREFIX properties to ""
+    # while keeping the default "liblzma" OUTPUT_NAME that was derived from
+    # the target name. But this broke naming on Cygwin and MSYS2.
+    #
+    # Setting OUTPUT_NAME without the "lib" prefix means that CMake will add
+    # the platform-specific prefix as needed. So on most systems CMake will
+    # add "lib" but on Cygwin and MSYS2 the naming will be correct too.
+    #
+    # On Windows, CMake uses the "lib" prefix with MinGW-w64 but not with
+    # other toolchains. Those those need to be handled specially to get
+    # the DLL file named liblzma.dll instead of lzma.dll.
+    OUTPUT_NAME "lzma"
 )
 
+if(WIN32 AND NOT MINGW)
+    # Up to XZ Utils 5.6.2 and building with MSVC, we produced liblzma.dll
+    # and liblzma.lib. The downside of liblzma.lib is that it's not
+    # compatible with pkgconf usage. liblzma.pc contains "-llzma" which
+    # "pkgconf --msvc-syntax --libs liblzma" converts to "lzma.lib".
+    # So as a compromise, we can keep the liblzma.dll name but the import
+    # library and static liblzma need to be named lzma.lib so that pkgconf
+    # can be used with MSVC. (MinGW-w64 finds both names with "-llzma".)
+    set_target_properties(liblzma PROPERTIES RUNTIME_OUTPUT_NAME "liblzma")
+endif()
+
 # Create liblzma-config-version.cmake.
 #
 # FIXME: SameMajorVersion is correct for stable releases but it is wrong