diff --git a/pyproject-rpm-macros.spec b/pyproject-rpm-macros.spec
index 4f90690..77e0ab7 100644
--- a/pyproject-rpm-macros.spec
+++ b/pyproject-rpm-macros.spec
@@ -107,6 +107,8 @@ export HOSTNAME="rpmbuild"  # to speedup tox in network-less mock, see rhbz#1856
 * Fri Jul 09 2021 Miro Hrončok <miro@hroncok.cz> - 0-44
 - Escape weird paths generated by %%pyproject_save_files
 - Fixes rhbz#1976363
+- Support x.* versions in %%pyproject_buildrequires
+- Fixes rhbz#1981558
 
 * Thu Jul 01 2021 Tomas Hrnciar <thrnciar@redhat.com> - 0-43
 - Generate BuildRequires from file
diff --git a/pyproject_buildrequires.py b/pyproject_buildrequires.py
index 0232126..42fd77a 100644
--- a/pyproject_buildrequires.py
+++ b/pyproject_buildrequires.py
@@ -2,7 +2,6 @@ import os
 import sys
 import importlib.metadata
 import argparse
-import functools
 import traceback
 import contextlib
 from io import StringIO
@@ -13,17 +12,23 @@ import tempfile
 import email.parser
 import pathlib
 
-print_err = functools.partial(print, file=sys.stderr)
 
 # Some valid Python version specifiers are not supported.
-# Whitelist characters we can handle.
-VERSION_RE = re.compile('[a-zA-Z0-9.-]+')
+# Allow only the forms we know we can handle.
+VERSION_RE = re.compile(r'[a-zA-Z0-9.-]+(\.\*)?')
 
 
 class EndPass(Exception):
     """End current pass of generating requirements"""
 
 
+# nb: we don't use functools.partial to be able to use pytest's capsys
+# see https://github.com/pytest-dev/pytest/issues/8900
+def print_err(*args, **kwargs):
+    kwargs.setdefault('file', sys.stderr)
+    print(*args, **kwargs)
+
+
 try:
     from packaging.requirements import Requirement, InvalidRequirement
     from packaging.utils import canonicalize_name
diff --git a/pyproject_buildrequires_testcases.yaml b/pyproject_buildrequires_testcases.yaml
index 7bc83d9..224503e 100644
--- a/pyproject_buildrequires_testcases.yaml
+++ b/pyproject_buildrequires_testcases.yaml
@@ -69,6 +69,24 @@ Bad character in version:
     requires = ["pkg == 0.$.^.*"]
   except: ValueError
 
+Single value version with unsupported compatible operator:
+  installed:
+    toml: 1
+  pyproject.toml: |
+    [build-system]
+    requires = ["pkg ~= 42"]
+  stderr_contains: "WARNING: Skipping invalid requirement: pkg ~= 42"
+  result: 0
+
+Asterisk in version with unsupported compatible operator:
+  installed:
+    toml: 1
+  pyproject.toml: |
+    [build-system]
+    requires = ["pkg ~= 0.1.*"]
+  stderr_contains: "WARNING: Skipping invalid requirement: pkg ~= 0.1.*"
+  result: 0
+
 Build system dependencies in pyproject.toml with extras:
   generate_extras: true
   installed:
@@ -88,6 +106,7 @@ Build system dependencies in pyproject.toml with extras:
         "compatible ~= 0.4.0",
         "equal == 0.5.0",
         "arbitrary_equal === 0.6.0",
+        "asterisk_equal == 0.6.*",
         "multi[Extras1,Extras2] == 6.0",
         "combo >2, <5, != 3.0.0",
         "invalid!!ignored",
@@ -106,6 +125,7 @@ Build system dependencies in pyproject.toml with extras:
     (python3dist(compatible) >= 0.4 with python3dist(compatible) < 0.5)
     python3dist(equal) = 0.5
     python3dist(arbitrary-equal) = 0.6
+    (python3dist(asterisk-equal) >= 0.6 with python3dist(asterisk-equal) < 0.7)
     python3dist(multi) = 6
     python3dist(multi[extras1]) = 6
     python3dist(multi[extras2]) = 6
diff --git a/test_pyproject_buildrequires.py b/test_pyproject_buildrequires.py
index 5170c29..4a7ebb2 100644
--- a/test_pyproject_buildrequires.py
+++ b/test_pyproject_buildrequires.py
@@ -57,8 +57,16 @@ def test_data(case_name, capsys, tmp_path, monkeypatch):
     else:
         assert 0 == case['result']
 
-        captured = capsys.readouterr()
-        assert captured.out == case['expected']
+        # this prevents us from accidentally writing "empty" tests
+        # if we ever need to do that, we can remove the check or change it:
+        assert 'expected' in case or 'stderr_contains' in case
+
+        out, err = capsys.readouterr()
+
+        if 'expected' in case:
+            assert out == case['expected']
+        if 'stderr_contains' in case:
+            assert case['stderr_contains'] in err
     finally:
         for req in requirement_files:
             req.close()