diff --git a/easybuild/easyblocks/generic/pythonbundle.py b/easybuild/easyblocks/generic/pythonbundle.py
index 01d9c4c672..73df0fd3a7 100644
--- a/easybuild/easyblocks/generic/pythonbundle.py
+++ b/easybuild/easyblocks/generic/pythonbundle.py
@@ -109,6 +109,15 @@ def prepare_step(self, *args, **kwargs):
 
             python_cmd = pick_python_cmd(req_maj_ver=req_py_majver, req_min_ver=req_py_minver)
 
+            # If pick_python_cmd didn't find a (system) Python command, we should raise an error
+            if python_cmd:
+                self.log.info("Python command being used: %s", python_cmd)
+            else:
+                raise EasyBuildError(
+                    "Failed to pick Python command that satisfies requirements in the easyconfig "
+                    "(req_py_majver = %s, req_py_minver = %s)", req_py_majver, req_py_minver
+                )
+
         self.all_pylibdirs = get_pylibdirs(python_cmd=python_cmd)
         self.pylibdir = self.all_pylibdirs[0]
 
diff --git a/easybuild/easyblocks/generic/pythonpackage.py b/easybuild/easyblocks/generic/pythonpackage.py
index f2ae208ebc..5ab60c6077 100644
--- a/easybuild/easyblocks/generic/pythonpackage.py
+++ b/easybuild/easyblocks/generic/pythonpackage.py
@@ -511,13 +511,23 @@ def prepare_python(self):
             # if using system Python, go hunting for a 'python' command that satisfies the requirements
             python = pick_python_cmd(req_maj_ver=req_py_majver, req_min_ver=req_py_minver)
 
-        if python:
+            # Check if we have Python by now. If not, and if self.require_python, raise a sensible error
+            if python:
+                self.python_cmd = python
+                self.log.info("Python command being used: %s", self.python_cmd)
+            elif self.require_python:
+                if req_py_majver is not None or req_py_minver is not None:
+                    raise EasyBuildError(
+                        "Failed to pick Python command that satisfies requirements in the easyconfig "
+                        "(req_py_majver = %s, req_py_minver = %s)", req_py_majver, req_py_minver
+                    )
+                else:
+                    raise EasyBuildError("Failed to pick Python command to use")
+            else:
+                self.log.warning("No Python command found!")
+        else:
             self.python_cmd = python
             self.log.info("Python command being used: %s", self.python_cmd)
-        elif self.require_python:
-            raise EasyBuildError("Failed to pick Python command to use")
-        else:
-            self.log.warning("No Python command found!")
 
         if self.python_cmd:
             # set Python lib directories