diff --git a/perl-Tk.spec b/perl-Tk.spec
index b5e9a2d..41fb01f 100644
--- a/perl-Tk.spec
+++ b/perl-Tk.spec
@@ -1,8 +1,11 @@
 %global use_x11_tests 1
+%if 0%{?fedora} || 0%{?rhel} > 9
+%global use_xwayland_run 1
+%endif
 
 Name:           perl-Tk
 Version:        804.036
-Release:        14%{?dist}
+Release:        15%{?dist}
 Summary:        Perl Graphical User Interface ToolKit
 
 License:        (GPL-1.0-or-later OR Artistic-1.0-Perl) AND SWL
@@ -74,7 +77,13 @@ BuildRequires:  perl(XSLoader)
 
 # Tests:
 # X11 tests:
+%if 0%{?use_xwayland_run}
+BuildRequires:  xwayland-run
+BuildRequires:  mutter
+BuildRequires:  mesa-dri-drivers
+%else
 BuildRequires:  xorg-x11-server-Xvfb
+%endif
 BuildRequires:  google-noto-sans-fonts
 BuildRequires:  font(:lang=en)
 # Specific font is needed for tests, bug #1141117, CPAN RT#98831
@@ -139,7 +148,13 @@ Summary:        Tests for %{name}
 Requires:       %{name} = %{?epoch:%{epoch}:}%{version}-%{release}
 Requires:       perl-Test-Harness
 # X11 tests:
+%if 0%{?use_xwayland_run}
+Requires:       xwayland-run
+Requires:       mutter
+Requires:       mesa-dri-drivers
+%else
 Requires:       xorg-x11-server-Xvfb
+%endif
 Requires:       google-noto-sans-fonts
 Requires:       font(:lang=en)
 Requires:       liberation-sans-fonts
@@ -181,7 +196,11 @@ find . -name Makefile | xargs perl -pi -e 's/^\tLD_RUN_PATH=[^\s]+\s*/\t/'
 
 %check
 %if %{use_x11_tests}
-    xvfb-run -d make test
+    %if 0%{?use_xwayland_run}
+        xwfb-run -c mutter -- make test
+    %else
+        xvfb-run -d make test
+    %endif
 %endif
 
 %install
@@ -210,7 +229,11 @@ set -e
 DIR=$(mktemp -d)
 pushd "$DIR"
 cp -a %{_libexecdir}/%{name}/* ./
-xvfb-run -d prove -I . -j "$(getconf _NPROCESSORS_ONLN)"
+%if 0%{?use_xwayland_run}
+    xwfb-run -c mutter -- prove -I . -j "$(getconf _NPROCESSORS_ONLN)"
+%else
+    xvfb-run -d prove -I . -j "$(getconf _NPROCESSORS_ONLN)"
+%endif
 popd
 rm -rf "$DIR"
 EOF
@@ -247,6 +270,10 @@ chmod +x %{buildroot}%{_libexecdir}/%{name}/test
 %{_libexecdir}/%{name}
 
 %changelog
+* Mon Jul 08 2024 Jitka Plesnikova <jplesnik@redhat.com> - 804.036-15
+- Resolves: RHEL-36643, RHEL-41058
+- Move away from xvfb-run
+
 * Mon Jun 24 2024 Troy Dawson <tdawson@redhat.com> - 804.036-14
 - Bump release for June 2024 mass rebuild
 
@@ -261,7 +288,7 @@ chmod +x %{buildroot}%{_libexecdir}/%{name}/test
 - Perl 5.38 rebuild
 
 * Thu Jun 01 2023 Michal Josef Špaček <mspacek@redhat.com> - 804.036-10
-- Fix %patch macro
+- Fix %%patch macro
 - Update license to SPDX format
 
 * Fri Feb 24 2023 Florian Weimer <fweimer@redhat.com> - 804.036-9
diff --git a/tests/upstream-tests.fmf b/tests/upstream-tests.fmf
index 3ceb8ad..165a0a8 100644
--- a/tests/upstream-tests.fmf
+++ b/tests/upstream-tests.fmf
@@ -7,9 +7,6 @@ test: /usr/libexec/perl-Tk/test
 enabled: true
 tag:
   - rhel-buildroot
-  - TestCaseCopy
-  - Tier1
-tier: '1'
 adjust:
   - enabled: false
     when: distro < rhel-9 or distro < centos-stream-9