diff --git a/doc/runner.rst b/doc/runner.rst
index da724864..6e9dbf4c 100644
--- a/doc/runner.rst
+++ b/doc/runner.rst
@@ -146,7 +146,7 @@ Option::
   There is no time out by default.
 * ``--tracemalloc``: Use the ``tracemalloc`` module to track Python memory
   allocation and get the peak of memory usage in metadata
-  (``tracemalloc_peak``). The module is only available on Python 3.4 and newer.
+  (``tracemalloc_peak``).
   See the `tracemalloc module
   <https://docs.python.org/dev/library/tracemalloc.html>`_.
 * ``--track-memory``: get the memory peak usage. it is less accurate than
diff --git a/pyperf/_cpu_utils.py b/pyperf/_cpu_utils.py
index f810df25..3199e845 100644
--- a/pyperf/_cpu_utils.py
+++ b/pyperf/_cpu_utils.py
@@ -17,20 +17,10 @@ def get_logical_cpu_count():
     if psutil is not None:
         # Number of logical CPUs
         cpu_count = psutil.cpu_count()
-    elif hasattr(os, 'cpu_count'):
+    else:
         # Python 3.4
+        # Python 3.13+: capped by -X cpu_count=n or $PYTHON_CPU_COUNT if set
         cpu_count = os.cpu_count()
-    else:
-        cpu_count = None
-        try:
-            import multiprocessing
-        except ImportError:
-            pass
-        else:
-            try:
-                cpu_count = multiprocessing.cpu_count()
-            except NotImplementedError:
-                pass
 
     if cpu_count is not None and cpu_count < 1:
         return None
@@ -148,7 +138,7 @@ def get_isolated_cpus():
 
 
 def set_cpu_affinity(cpus):
-    # Python 3.3 or newer?
+    # Availability: some Unix platforms
     if hasattr(os, 'sched_setaffinity'):
         os.sched_setaffinity(0, cpus)
         return True
@@ -161,6 +151,8 @@ def set_cpu_affinity(cpus):
     except ImportError:
         return
 
+    # Availability: Linux, Windows, FreeBSD (psutil 2.2.0+)
+    # https://psutil.rtfd.io/en/latest/index.html#psutil.Process.cpu_affinity
     proc = psutil.Process()
     if not hasattr(proc, 'cpu_affinity'):
         return
diff --git a/pyperf/_runner.py b/pyperf/_runner.py
index 8000bc60..d87a2f69 100644
--- a/pyperf/_runner.py
+++ b/pyperf/_runner.py
@@ -416,12 +416,14 @@ def _cpu_affinity(self):
         else:
             if not isolated:
                 print("ERROR: CPU affinity not available.", file=sys.stderr)
-                print("Use Python 3.3 or newer, or install psutil dependency")
+                print("Install psutil dependency and check "
+                      "psutil.Process.cpu_affinity is available on your OS.")
                 sys.exit(1)
             elif not self.args.quiet:
                 print("WARNING: unable to pin worker processes to "
                       "isolated CPUs, CPU affinity not available")
-                print("Use Python 3.3 or newer, or install psutil dependency")
+                print("Install psutil dependency and check "
+                      "psutil.Process.cpu_affinity is available on your OS.")
 
     def _process_priority(self):
         if not MS_WINDOWS:
diff --git a/pyperf/_utils.py b/pyperf/_utils.py
index ef542d9d..540e7eed 100644
--- a/pyperf/_utils.py
+++ b/pyperf/_utils.py
@@ -174,22 +174,7 @@ def sysfs_path(path):
 
 
 def python_implementation():
-    if hasattr(sys, 'implementation'):
-        # PEP 421, Python 3.3
-        name = sys.implementation.name
-    else:
-        # Code extracted from platform.python_implementation().
-        # Don't import platform to avoid the subprocess import.
-        sys_version = sys.version
-        if 'IronPython' in sys_version:
-            name = 'IronPython'
-        elif sys.platform.startswith('java'):
-            name = 'Jython'
-        elif "PyPy" in sys_version:
-            name = "PyPy"
-        else:
-            name = 'CPython'
-    return name.lower()
+    return sys.implementation.name.lower()
 
 
 def python_has_jit():