diff --git a/pyelftools.spec b/pyelftools.spec
index 3f97019..9f0345d 100644
--- a/pyelftools.spec
+++ b/pyelftools.spec
@@ -18,6 +18,9 @@
 %global         with_python3 1
 %endif
 
+# main package is archful to run tests everywhere but produces noarch packages
+%global         debug_package %{nil}
+
 Summary:        Pure-Python library for parsing and analyzing ELF files
 Name:           pyelftools
 Version:        0.26
@@ -27,15 +30,6 @@ URL:            https://github.com/eliben/pyelftools
 # https://github.com/eliben/pyelftools/issues/260
 #Source0:        https://files.pythonhosted.org/packages/source/p/pyelftools/pyelftools-%{version}.tar.gz
 Source0:        https://github.com/eliben/pyelftools/archive/v%{version}/%{name}-%{version}.tar.gz
-%if 0%{?with_python2}
-BuildRequires:  python2-devel
-BuildRequires:  python2-setuptools
-%endif
-%if 0%{?with_python3}
-BuildRequires:  python3-devel
-BuildRequires:  python3-setuptools
-%endif
-BuildArch:      noarch
 %global _description \
 Pure-Python library for parsing and analyzing ELF files\
 and DWARF debugging information.
@@ -45,6 +39,9 @@ and DWARF debugging information.
 %package     -n python2-%{name}
 Summary:        %{summary}
 Requires:       python2-construct
+BuildRequires:  python2-devel
+BuildRequires:  python2-setuptools
+BuildArch:      noarch
 %{?python_provide:%python_provide python2-%{name}}
 # Remove before F30
 %description -n python2-%{name} %_description
@@ -54,6 +51,9 @@ Requires:       python2-construct
 %package     -n python3-%{name}
 Summary:	%{summary}
 Requires:	python3-construct
+BuildRequires:  python3-devel
+BuildRequires:  python3-setuptools
+BuildArch:      noarch
 %{?python_provide:%python_provide python3-%{name}}
 %description -n python3-%{name} %_description
 %endif
@@ -83,17 +83,21 @@ mv %{buildroot}/usr/bin/readelf.py %{buildroot}/usr/bin/%{py3readelf}
 %if 0%{?with_python2}
 %{__python2} test/run_all_unittests.py
 %{__python2} test/run_examples_test.py
+%ifarch x86_64
 # tests may fail because of differences in output-formatting
 # from binutils' readelf.  See:
 # https://github.com/eliben/pyelftools/wiki/Hacking-guide#tests
 %{__python2} test/run_readelf_tests.py || :
 %endif
+%endif
 %if 0%{?with_python3}
 %{__python3} test/run_all_unittests.py
 %{__python3} test/run_examples_test.py
+%ifarch x86_64
 # ditto
 %{__python3} test/run_readelf_tests.py || :
 %endif
+%endif
 
 %if 0%{?with_python2}
 %files -n python2-%{name}
@@ -116,6 +120,9 @@ mv %{buildroot}/usr/bin/readelf.py %{buildroot}/usr/bin/%{py3readelf}
 %changelog
 * Tue Dec 17 2019 Dominik Mierzejewski <rpm@greysector.net> - 0.26-1
 - update to 0.26 (#1780153)
+- make main package archful to run tests on all arches
+  (pythonN-pyelftools subpackages are still noarch)
+- run readelf tests on x86_64 only for now
 
 * Thu Oct 03 2019 Miro Hrončok <mhroncok@redhat.com> - 0.25-5
 - Rebuilt for Python 3.8.0rc1 (#1748018)