diff --git a/cmake.spec b/cmake.spec
index 66cabb5..fdb50ad 100644
--- a/cmake.spec
+++ b/cmake.spec
@@ -200,6 +200,11 @@ Provides: bundled(md5-deutsch)
 # https://fedorahosted.org/fpc/ticket/555
 Provides: bundled(kwsys)
 
+# The license files are shipped in both the cmake and cmake-doc packages and
+# can cause conflicts when updating.
+# See https://lists.fedoraproject.org/archives/list/devel@lists.fedoraproject.org/thread/JDSG4K2S3IRCSZ37WCUGABY3JA45QMVA/#GEZTXMP5SXNMGAT3JPXDSQM5FPOLUJ5K
+Conflicts: cmake-doc < %{version}-%{release}
+
 %description
 CMake is used to control the software compilation process using simple
 platform and compiler independent configuration files. CMake generates
@@ -231,8 +236,10 @@ This package contains common data-files for %{name}.
 Summary:        Documentation for %{name}
 BuildArch:      noarch
 
-# license files moved from the doc package to main package.
-Conflicts:      %{name} <= 3.20.1
+# The license files are shipped in both the cmake and cmake-doc packages and
+# can cause conflicts when updating.
+# See https://lists.fedoraproject.org/archives/list/devel@lists.fedoraproject.org/thread/JDSG4K2S3IRCSZ37WCUGABY3JA45QMVA/#GEZTXMP5SXNMGAT3JPXDSQM5FPOLUJ5K
+Conflicts:      %{name} < %{version}-%{release}
 
 %description    doc
 This package contains documentation for %{name}.