diff --git a/src/ufonormalizer/__init__.py b/src/ufonormalizer/__init__.py
index 2c8b5c5..cb4f133 100644
--- a/src/ufonormalizer/__init__.py
+++ b/src/ufonormalizer/__init__.py
@@ -12,6 +12,7 @@
 from collections import OrderedDict
 from io import open
 import logging
+import sys
 
 try:
     from ._version import __version__
@@ -46,7 +47,7 @@ def main(args=None):
     parser = argparse.ArgumentParser(description=description)
     parser.add_argument("input",
                         help="Path to a UFO to normalize.",
-                        nargs="?")
+                        nargs="+")
     parser.add_argument("-t", "--test",
                         help="Run the normalizer's internal tests.",
                         action="store_true")
@@ -85,16 +86,17 @@ def main(args=None):
     logLevel = "DEBUG" if args.verbose else "ERROR" if args.quiet else "INFO"
     logging.basicConfig(level=logLevel, format="%(message)s")
 
-    if args.input is None:
-        parser.error("No input path was specified.")
-    inputPath = os.path.normpath(args.input)
-    outputPath = args.output
-    onlyModified = not args.all
-    if not os.path.exists(inputPath):
-        parser.error(f'Input path does not exist: "{ inputPath }".')
-    if os.path.splitext(inputPath)[-1].lower() != ".ufo":
-        parser.error(f'Input path is not a UFO: "{ inputPath }".')
+    if len(args.input) > 1 and args.output:
+        parser.error("can't use -o/--output with multiple input UFOs")
+    elif len(args.input) == 1:
+        inputPath = os.path.normpath(args.input[0])
+        inputPaths = [inputPath]
+        outputPaths = [args.output or inputPath]
+    else:
+        inputPaths = [os.path.normpath(inputPath) for inputPath in args.input]
+        outputPaths = inputPaths
 
+    onlyModified = not args.all
     if args.float_precision >= 0:
         floatPrecision = args.float_precision
     elif args.float_precision == -1:
@@ -104,16 +106,28 @@ def main(args=None):
 
     writeModTimes = not args.no_mod_times
 
+    allSkipped = True
     message = 'Normalizing "%s".'
-    if not onlyModified:
-        message += " Processing all files."
-    log.info(message, os.path.basename(inputPath))
-    start = time.time()
-    normalizeUFO(inputPath, outputPath=outputPath, onlyModified=onlyModified,
-                 floatPrecision=floatPrecision, writeModTimes=writeModTimes)
-    runtime = time.time() - start
-    log.info("Normalization complete (%.4f seconds).", runtime)
-
+    for inputPath, outputPath in zip(inputPaths, outputPaths):
+        if not os.path.exists(inputPath):
+            log.error(f'Skipping non-existent input path: "{ inputPath }".')
+            continue
+        if os.path.splitext(inputPath)[-1].lower() != ".ufo":
+            log.error(f'Skipping input path that isn\'t a UFO: "{ inputPath }".')
+            continue
+        allSkipped = False
+
+        if not onlyModified:
+            message += " Processing all files."
+        log.info(message, os.path.basename(inputPath))
+        start = time.time()
+        normalizeUFO(inputPath, outputPath=outputPath, onlyModified=onlyModified,
+                    floatPrecision=floatPrecision, writeModTimes=writeModTimes)
+        runtime = time.time() - start
+        log.info("Normalization complete (%.4f seconds).", runtime)
+
+    if allSkipped:
+        sys.exit(2)
 
 # ---------
 # Internals
diff --git a/tests/test_ufonormalizer.py b/tests/test_ufonormalizer.py
index b256e9f..b8ad8f1 100644
--- a/tests/test_ufonormalizer.py
+++ b/tests/test_ufonormalizer.py
@@ -33,6 +33,8 @@
 from io import StringIO
 from tempfile import TemporaryDirectory
 
+import ufonormalizer
+
 GLIFFORMAT1 = '''\
 <?xml version="1.0" encoding="UTF-8"?>
 <glyph name="period" format="1">
@@ -196,6 +198,11 @@ def __init__(self, methodName):
         if not hasattr(self, "assertRaisesRegex"):
             self.assertRaisesRegex = self.assertRaisesRegexp
 
+    def assertLogsContain(self, logsContext, phrase):
+        self.assertTrue(
+            any(phrase in logLine for logLine in logsContext.output)
+        )
+
     def _test_normalizeGlyphsDirectoryNames(self, oldLayers, expectedLayers):
         directory = tempfile.mkdtemp()
         for _layerName, subDirectory in oldLayers:
@@ -1413,23 +1420,28 @@ def test_main_no_path(self):
         with self.assertRaisesRegex(SystemExit, '2'):
             with redirect_stderr(stream):
                 main([])
-        self.assertTrue("No input path" in stream.getvalue())
+        self.assertIn("the following arguments are required: input", stream.getvalue())
 
     def test_main_input_does_not_exist(self):
-        stream = StringIO()
-        with self.assertRaisesRegex(SystemExit, '2'):
-            with redirect_stderr(stream):
+        with self.assertLogs(ufonormalizer.__name__, level="ERROR") as logs:
+            with self.assertRaisesRegex(SystemExit, '2'):
                 main(['foobarbazquz'])
-        self.assertTrue("Input path does not exist" in stream.getvalue())
+            self.assertLogsContain(logs, "Skipping non-existent input path")
 
     def test_main_input_not_ufo(self):
         # I use the path to the test module itself
         existing_not_ufo_file = os.path.realpath(__file__)
+        with self.assertLogs(ufonormalizer.__name__, level="ERROR") as logs:
+            with self.assertRaisesRegex(SystemExit, '2'):
+                main([existing_not_ufo_file])
+            self.assertLogsContain(logs, "Skipping input path that isn't a UFO")
+
+    def test_main_multiple_inputs_and_output(self):
         stream = StringIO()
         with self.assertRaisesRegex(SystemExit, '2'):
             with redirect_stderr(stream):
-                main([existing_not_ufo_file])
-        self.assertTrue("Input path is not a UFO" in stream.getvalue())
+                main(['--output', 'foo', 'bar', 'baz'])
+        self.assertIn("can't use -o/--output with multiple input UFOs", stream.getvalue())
 
     def test_main_invalid_float_precision(self):
         stream = StringIO()