diff --git a/distutils/command/bdist_rpm.py b/distutils/command/bdist_rpm.py
index 649968a5..03bb0f3a 100644
--- a/distutils/command/bdist_rpm.py
+++ b/distutils/command/bdist_rpm.py
@@ -316,11 +316,13 @@ def run(self):  # noqa: C901
 
         source = sdist.get_archive_files()[0]
         source_dir = rpm_dir['SOURCES']
-        self.copy_file(source, source_dir)
+        dest = os.path.join(source_dir, os.path.basename(source))
+        self.copy_file(source, dest)
 
         if self.icon:
             if os.path.exists(self.icon):
-                self.copy_file(self.icon, source_dir)
+                dest = os.path.join(source_dir, os.path.basename(self.icon))
+                self.copy_file(self.icon, dest)
             else:
                 raise DistutilsFileError("icon file '%s' does not exist" % self.icon)
 
diff --git a/distutils/command/install_data.py b/distutils/command/install_data.py
index b63a1af2..cc6ac697 100644
--- a/distutils/command/install_data.py
+++ b/distutils/command/install_data.py
@@ -54,7 +54,8 @@ def run(self):
                         "setup script did not provide a directory for "
                         f"'{f}' -- installing right in '{self.install_dir}'"
                     )
-                (out, _) = self.copy_file(f, self.install_dir)
+                dst = os.path.join(self.install_dir, os.path.basename(f))
+                (out, _) = self.copy_file(f, dst)
                 self.outfiles.append(out)
             else:
                 # it's a tuple with path to install to and a list of files
@@ -74,7 +75,8 @@ def run(self):
                     # Copy files, adding them to the list of output files.
                     for data in f[1]:
                         data = convert_path(data)
-                        (out, _) = self.copy_file(data, dir)
+                        dst = os.path.join(dir, os.path.basename(data))
+                        (out, _) = self.copy_file(data, dst)
                         self.outfiles.append(out)
 
     def get_inputs(self):
diff --git a/distutils/command/install_headers.py b/distutils/command/install_headers.py
index 085272c1..b7fb4b41 100644
--- a/distutils/command/install_headers.py
+++ b/distutils/command/install_headers.py
@@ -3,6 +3,8 @@
 Implements the Distutils 'install_headers' command, to install C/C++ header
 files to the Python include directory."""
 
+import os
+
 from ..core import Command
 
 
@@ -34,7 +36,8 @@ def run(self):
 
         self.mkpath(self.install_dir)
         for header in headers:
-            (out, _) = self.copy_file(header, self.install_dir)
+            dst = os.path.join(self.install_dir, os.path.basename(header))
+            (out, _) = self.copy_file(header, dst)
             self.outfiles.append(out)
 
     def get_inputs(self):
diff --git a/distutils/file_util.py b/distutils/file_util.py
index 960def9c..e2239ac7 100644
--- a/distutils/file_util.py
+++ b/distutils/file_util.py
@@ -70,9 +70,8 @@ def copy_file(  # noqa: C901
     verbose=1,
     dry_run=0,
 ):
-    """Copy a file 'src' to 'dst'.  If 'dst' is a directory, then 'src' is
-    copied there with the same name; otherwise, it must be a filename.  (If
-    the file exists, it will be ruthlessly clobbered.)  If 'preserve_mode'
+    """Copy a file 'src' to 'dst'.
+    (If the file exists, it will be ruthlessly clobbered.)  If 'preserve_mode'
     is true (the default), the file's mode (type and permission bits, or
     whatever is analogous on the current platform) is copied.  If
     'preserve_times' is true (the default), the last-modified and
@@ -109,12 +108,6 @@ def copy_file(  # noqa: C901
             "can't copy '%s': doesn't exist or not a regular file" % src
         )
 
-    if os.path.isdir(dst):
-        dir = dst
-        dst = os.path.join(dst, os.path.basename(src))
-    else:
-        dir = os.path.dirname(dst)
-
     if update and not newer(src, dst):
         if verbose >= 1:
             log.debug("not copying %s (output up-to-date)", src)
@@ -126,10 +119,7 @@ def copy_file(  # noqa: C901
         raise ValueError("invalid value '%s' for 'link' argument" % link)
 
     if verbose >= 1:
-        if os.path.basename(dst) == os.path.basename(src):
-            log.info("%s %s -> %s", action, src, dir)
-        else:
-            log.info("%s %s -> %s", action, src, dst)
+        log.info("%s %s -> %s", action, src, dst)
 
     if dry_run:
         return (dst, 1)
diff --git a/distutils/tests/test_dir_util.py b/distutils/tests/test_dir_util.py
index 84cda619..8d4dc9fd 100644
--- a/distutils/tests/test_dir_util.py
+++ b/distutils/tests/test_dir_util.py
@@ -73,9 +73,10 @@ def test_copy_tree_verbosity(self, caplog):
 
         mkpath(self.target, verbose=0)
         a_file = path.Path(self.target) / 'ok.txt'
+        to_file = path.Path(self.target2) / 'ok.txt'
         jaraco.path.build({'ok.txt': 'some content'}, self.target)
 
-        wanted = [f'copying {a_file} -> {self.target2}']
+        wanted = [f'copying {a_file} -> {to_file}']
         copy_tree(self.target, self.target2, verbose=1)
         assert caplog.messages == wanted