diff --git a/flit_core/flit_core/_spdx_data.py b/flit_core/flit_core/_spdx_data.py
index 5af71dbb..38b32bef 100644
--- a/flit_core/flit_core/_spdx_data.py
+++ b/flit_core/flit_core/_spdx_data.py
@@ -649,3 +649,80 @@
  'zpl-1.1': {'id': 'ZPL-1.1'},
  'zpl-2.0': {'id': 'ZPL-2.0'},
  'zpl-2.1': {'id': 'ZPL-2.1'}}
+exceptions = \
+{'389-exception': {'id': '389-exception'},
+ 'asterisk-exception': {'id': 'Asterisk-exception'},
+ 'asterisk-linking-protocols-exception': {'id': 'Asterisk-linking-protocols-exception'},
+ 'autoconf-exception-2.0': {'id': 'Autoconf-exception-2.0'},
+ 'autoconf-exception-3.0': {'id': 'Autoconf-exception-3.0'},
+ 'autoconf-exception-generic': {'id': 'Autoconf-exception-generic'},
+ 'autoconf-exception-generic-3.0': {'id': 'Autoconf-exception-generic-3.0'},
+ 'autoconf-exception-macro': {'id': 'Autoconf-exception-macro'},
+ 'bison-exception-1.24': {'id': 'Bison-exception-1.24'},
+ 'bison-exception-2.2': {'id': 'Bison-exception-2.2'},
+ 'bootloader-exception': {'id': 'Bootloader-exception'},
+ 'cgal-linking-exception': {'id': 'CGAL-linking-exception'},
+ 'classpath-exception-2.0': {'id': 'Classpath-exception-2.0'},
+ 'clisp-exception-2.0': {'id': 'CLISP-exception-2.0'},
+ 'cryptsetup-openssl-exception': {'id': 'cryptsetup-OpenSSL-exception'},
+ 'digirule-foss-exception': {'id': 'DigiRule-FOSS-exception'},
+ 'ecos-exception-2.0': {'id': 'eCos-exception-2.0'},
+ 'erlang-otp-linking-exception': {'id': 'erlang-otp-linking-exception'},
+ 'fawkes-runtime-exception': {'id': 'Fawkes-Runtime-exception'},
+ 'fltk-exception': {'id': 'FLTK-exception'},
+ 'fmt-exception': {'id': 'fmt-exception'},
+ 'font-exception-2.0': {'id': 'Font-exception-2.0'},
+ 'freertos-exception-2.0': {'id': 'freertos-exception-2.0'},
+ 'gcc-exception-2.0': {'id': 'GCC-exception-2.0'},
+ 'gcc-exception-2.0-note': {'id': 'GCC-exception-2.0-note'},
+ 'gcc-exception-3.1': {'id': 'GCC-exception-3.1'},
+ 'gmsh-exception': {'id': 'Gmsh-exception'},
+ 'gnat-exception': {'id': 'GNAT-exception'},
+ 'gnome-examples-exception': {'id': 'GNOME-examples-exception'},
+ 'gnu-compiler-exception': {'id': 'GNU-compiler-exception'},
+ 'gnu-javamail-exception': {'id': 'gnu-javamail-exception'},
+ 'gpl-3.0-389-ds-base-exception': {'id': 'GPL-3.0-389-ds-base-exception'},
+ 'gpl-3.0-interface-exception': {'id': 'GPL-3.0-interface-exception'},
+ 'gpl-3.0-linking-exception': {'id': 'GPL-3.0-linking-exception'},
+ 'gpl-3.0-linking-source-exception': {'id': 'GPL-3.0-linking-source-exception'},
+ 'gpl-cc-1.0': {'id': 'GPL-CC-1.0'},
+ 'gstreamer-exception-2005': {'id': 'GStreamer-exception-2005'},
+ 'gstreamer-exception-2008': {'id': 'GStreamer-exception-2008'},
+ 'harbour-exception': {'id': 'harbour-exception'},
+ 'i2p-gpl-java-exception': {'id': 'i2p-gpl-java-exception'},
+ 'independent-modules-exception': {'id': 'Independent-modules-exception'},
+ 'kicad-libraries-exception': {'id': 'KiCad-libraries-exception'},
+ 'lgpl-3.0-linking-exception': {'id': 'LGPL-3.0-linking-exception'},
+ 'libpri-openh323-exception': {'id': 'libpri-OpenH323-exception'},
+ 'libtool-exception': {'id': 'Libtool-exception'},
+ 'linux-syscall-note': {'id': 'Linux-syscall-note'},
+ 'llgpl': {'id': 'LLGPL'},
+ 'llvm-exception': {'id': 'LLVM-exception'},
+ 'lzma-exception': {'id': 'LZMA-exception'},
+ 'mif-exception': {'id': 'mif-exception'},
+ 'mxml-exception': {'id': 'mxml-exception'},
+ 'ocaml-lgpl-linking-exception': {'id': 'OCaml-LGPL-linking-exception'},
+ 'occt-exception-1.0': {'id': 'OCCT-exception-1.0'},
+ 'openjdk-assembly-exception-1.0': {'id': 'OpenJDK-assembly-exception-1.0'},
+ 'openvpn-openssl-exception': {'id': 'openvpn-openssl-exception'},
+ 'pcre2-exception': {'id': 'PCRE2-exception'},
+ 'ps-or-pdf-font-exception-20170817': {'id': 'PS-or-PDF-font-exception-20170817'},
+ 'qpl-1.0-inria-2004-exception': {'id': 'QPL-1.0-INRIA-2004-exception'},
+ 'qt-gpl-exception-1.0': {'id': 'Qt-GPL-exception-1.0'},
+ 'qt-lgpl-exception-1.1': {'id': 'Qt-LGPL-exception-1.1'},
+ 'qwt-exception-1.0': {'id': 'Qwt-exception-1.0'},
+ 'romic-exception': {'id': 'romic-exception'},
+ 'rrdtool-floss-exception-2.0': {'id': 'RRDtool-FLOSS-exception-2.0'},
+ 'sane-exception': {'id': 'SANE-exception'},
+ 'shl-2.0': {'id': 'SHL-2.0'},
+ 'shl-2.1': {'id': 'SHL-2.1'},
+ 'stunnel-exception': {'id': 'stunnel-exception'},
+ 'swi-exception': {'id': 'SWI-exception'},
+ 'swift-exception': {'id': 'Swift-exception'},
+ 'texinfo-exception': {'id': 'Texinfo-exception'},
+ 'u-boot-exception-2.0': {'id': 'u-boot-exception-2.0'},
+ 'ubdl-exception': {'id': 'UBDL-exception'},
+ 'universal-foss-exception-1.0': {'id': 'Universal-FOSS-exception-1.0'},
+ 'vsftpd-openssl-exception': {'id': 'vsftpd-openssl-exception'},
+ 'wxwindows-exception-3.1': {'id': 'WxWindows-exception-3.1'},
+ 'x11vnc-openssl-exception': {'id': 'x11vnc-openssl-exception'}}
diff --git a/flit_core/flit_core/config.py b/flit_core/flit_core/config.py
index e1e55b91..3f2c09d3 100644
--- a/flit_core/flit_core/config.py
+++ b/flit_core/flit_core/config.py
@@ -17,7 +17,7 @@
     except ImportError:
         import tomli as tomllib
 
-from ._spdx_data import licenses
+from ._spdx_data import exceptions, licenses
 from .common import normalise_core_metadata_name
 from .versionno import normalise_version
 
@@ -700,7 +700,7 @@ def normalise_compound_license_expr(s: str) -> str:
     """Validate and normalise a compound SPDX license expression.
 
     Per the specification, licence expression operators (AND, OR and WITH)
-    are matched case-sensitively. The WITH operator is not currently supported.
+    are matched case-sensitively.
 
     Spec: https://spdx.github.io/spdx-spec/v2.2.2/SPDX-license-expressions/
     """
@@ -712,9 +712,15 @@ def normalise_compound_license_expr(s: str) -> str:
     parts = []
     try:
         for part in filter(None, re.split(r' +|([()])', s)):
-            if part.upper() == 'WITH':
-                # provide a sensible error message for the WITH operator
-                raise ConfigError("The SPDX 'WITH' operator is not yet supported!")
+            if part == 'WITH':
+                if (
+                    not parts
+                    or parts[-1] in {' AND ', ' OR ', ' WITH ', '('}
+                    or parts[-1].lower() in exceptions
+                ):
+                    reason = "a license ID is missing before 'WITH'"
+                    raise ConfigError(invalid_msg.format(s=s, reason=reason))
+                parts.append(' WITH ')
             elif part in {'AND', 'OR'}:
                 if not parts or parts[-1] in {' AND ', ' OR ', ' WITH ', '('}:
                     reason = f"a license ID is missing before '{part}'"
@@ -740,10 +746,13 @@ def normalise_compound_license_expr(s: str) -> str:
                     raise ConfigError(invalid_msg.format(s=s, reason=reason))
                 parts.append(part)
             else:
-                if parts and parts[-1] not in {' AND ', ' OR ', '('}:
+                if parts and parts[-1] not in {' AND ', ' OR ', ' WITH ', '('}:
                     reason = "a license ID must follow either AND, OR, or '('"
                     raise ConfigError(invalid_msg.format(s=s, reason=reason))
-                simple_expr = normalise_simple_license_expr(part)
+                if parts and parts[-1] == ' WITH ':
+                    simple_expr = normalise_license_exception(part)
+                else:
+                    simple_expr = normalise_simple_license_expr(part)
                 parts.append(simple_expr)
 
         if stack != 0:
@@ -790,3 +799,11 @@ def normalise_simple_license_expr(s: str) -> str:
     if or_later:
         return f'{normalised_id}+'
     return normalised_id
+
+
+def normalise_license_exception(s: str) -> str:
+    """Normalise an SPDX license exception ID."""
+    try:
+        return exceptions[s.lower()]['id']
+    except KeyError:
+        raise ConfigError(f"{s!r} is not a recognised SPDX license exception ID")
diff --git a/flit_core/tests_core/test_config.py b/flit_core/tests_core/test_config.py
index 5270696c..36b49196 100644
--- a/flit_core/tests_core/test_config.py
+++ b/flit_core/tests_core/test_config.py
@@ -218,6 +218,8 @@ def test_bad_pep621_readme(readme, err_match):
     ("MIT AND Apache-2.0", "MIT AND Apache-2.0"),
     ("MIT AND Apache-2.0+ OR 0BSD", "MIT AND Apache-2.0+ OR 0BSD"),
     ("MIT AND (Apache-2.0+ OR (0BSD))", "MIT AND (Apache-2.0+ OR (0BSD))"),
+    ("mit WITH classpath-exception-2.0", "MIT WITH Classpath-exception-2.0"),
+    ("MIT OR MIT WITH Classpath-exception-2.0", "MIT OR MIT WITH Classpath-exception-2.0"),
     ("MIT OR(mit)", "MIT OR (MIT)"),
     ("(mit)AND mit", "(MIT) AND MIT"),
     ("MIT OR (MIT OR ( MIT )) AND ((MIT) AND MIT) OR MIT", "MIT OR (MIT OR (MIT)) AND ((MIT) AND MIT) OR MIT"),
@@ -342,6 +344,7 @@ def test_license_expr_error_empty(invalid_expr: str):
     "MIT and MIT",
     "MIT AND MIT or MIT",
     "MIT AND (MIT or MIT)",
+    "MIT with Classpath-exception-2.0",
 ])
 def test_license_expr_error_lowercase(invalid_expr: str):
     proj = {
@@ -360,14 +363,18 @@ def test_license_expr_error_lowercase(invalid_expr: str):
     "MIT WITH MIT-Exception",
     "(MIT WITH MIT-Exception)",
     "MIT OR MIT WITH MIT-Exception",
+    "MIT WITH Classpath-exception-2.0 WITH Autoconf-exception-2.0",
     "MIT WITH MIT-Exception OR (MIT AND MIT)",
 ])
-def test_license_expr_error_unsupported_with(invalid_expr: str):
+def test_license_expr_error_with(invalid_expr: str):
     proj = {
         'name': 'module1', 'version': '1.0', 'description': 'x',
         'license': invalid_expr,
     }
-    with pytest.raises(config.ConfigError, match="not yet supported"):
+    with pytest.raises(
+        config.ConfigError,
+        match="(license ID is missing before|must be uppercase|not a recognised SPDX license exception ID)",
+    ):
         config.read_pep621_metadata(proj, samples_dir / 'pep621' / 'pyproject.toml')
 
 
diff --git a/prepare_license_list.py b/prepare_license_list.py
index 8f8476e5..49441bdd 100644
--- a/prepare_license_list.py
+++ b/prepare_license_list.py
@@ -9,15 +9,23 @@
 list_data_repo = Path(sys.argv[1])
 with (list_data_repo / 'json' / 'licenses.json').open('rb') as f:
     licenses_json = json.load(f)
+with (list_data_repo / 'json' / 'exceptions.json').open('rb') as f:
+    exceptions_json = json.load(f)
 
-condensed = {
+licenses = {
     l['licenseId'].lower(): {'id': l['licenseId']}
     for l in licenses_json['licenses']
     if not l['isDeprecatedLicenseId']
 }
+exceptions = {
+    e['licenseExceptionId'].lower(): {'id': e['licenseExceptionId']}
+    for e in exceptions_json['exceptions']
+    if not e['isDeprecatedLicenseId']
+}
 
 with Path('flit_core', 'flit_core', '_spdx_data.py').open('w') as f:
     f.write("# This file is generated from SPDX license data; don't edit it manually.\n\n")
 
-    f.write("licenses = \\\n")
-    pprint.pprint(condensed, f)
+    for name, data in (("licenses", licenses), ("exceptions", exceptions)):
+        f.write(f"{name} = \\\n")
+        pprint.pprint(data, f)