diff --git a/packaging/linux/fedora/Sunshine.spec b/packaging/linux/fedora/Sunshine.spec
index c19ddf78c90..4211063142c 100644
--- a/packaging/linux/fedora/Sunshine.spec
+++ b/packaging/linux/fedora/Sunshine.spec
@@ -54,7 +54,7 @@ BuildRequires: which
 BuildRequires: xorg-x11-server-Xvfb
 
 # Conditional BuildRequires for cuda-gcc based on Fedora version
-%if 0%{?fedora} >= 40
+%if 0%{?fedora} > 39
 # this package conflicts with gcc on f39
 BuildRequires: cuda-gcc-c++
 %endif
@@ -95,14 +95,12 @@ fedora_version=%{fedora}
 cuda_supported_architectures=("x86_64" "aarch64")
 
 # set cuda_version based on Fedora version
-# these are the same right now, but leave this structure to make it easier to set different versions
-if [ "$fedora_version" == 39 ]; then
-  cuda_version="12.6.2"
-  cuda_build="560.35.03"
-else
-  cuda_version="12.6.2"
-  cuda_build="560.35.03"
-fi
+case "$fedora_version" in
+  *)
+    cuda_version="12.6.3"
+    cuda_build="560.35.05"
+    ;;
+esac
 
 # prepare CMAKE args
 cmake_args=(