diff --git a/docs/markdown/Reference-manual.md b/docs/markdown/Reference-manual.md
index aedfda1cd..de7f9f26f 100644
--- a/docs/markdown/Reference-manual.md
+++ b/docs/markdown/Reference-manual.md
@@ -2554,7 +2554,9 @@ module](#shared_module).
   object files generated for those source files. This is typically used
   to take single object files and link them to unit tests or to compile
   some source files with custom flags. To use the object file(s)
-  in another build target, use the `objects:` keyword argument.
+  in another build target, use the [`objects:`](#executable) keyword
+  argument or include them in the command line of a
+  [`custom_target`](#custom_target)`.
 
 - `full_path()`: returns a full path pointing to the result target file.
   NOTE: In most cases using the object itself will do the same job as
diff --git a/mesonbuild/build.py b/mesonbuild/build.py
index 414a4f814..03f97b224 100644
--- a/mesonbuild/build.py
+++ b/mesonbuild/build.py
@@ -378,7 +378,8 @@ class ExtractedObjects(HoldableObject):
         r = '<{0} {1!r}: {2}>'
         return r.format(self.__class__.__name__, self.target.name, self.srclist)
 
-    def classify_all_sources(self, sources, generated_sources):
+    @staticmethod
+    def get_sources(sources, generated_sources):
         # Merge sources and generated sources
         sources = list(sources)
         for gensrc in generated_sources:
@@ -389,8 +390,10 @@ class ExtractedObjects(HoldableObject):
                 sources.append(s)
 
         # Filter out headers and all non-source files
-        sources = [s for s in sources if environment.is_source(s) and not environment.is_header(s)]
+        return [s for s in sources if environment.is_source(s) and not environment.is_header(s)]
 
+    def classify_all_sources(self, sources, generated_sources):
+        sources = self.get_sources(sources, generated_sources)
         return classify_unity_sources(self.target.compilers.values(), sources)
 
     def check_unity_compatible(self):
@@ -410,10 +413,9 @@ class ExtractedObjects(HoldableObject):
                                      'the object files for each compiler at once.')
 
     def get_outputs(self, backend):
-        # TODO: Consider if we need to handle genlist here
         return [
             backend.object_filename_from_source(self.target, source)
-            for source in self.srclist
+            for source in self.get_sources(self.srclist, self.genlist)
         ]
 
 class EnvironmentVariables(HoldableObject):
diff --git a/test cases/common/22 object extraction/check-obj.py b/test cases/common/22 object extraction/check-obj.py
new file mode 100644
index 000000000..99c2cc546
--- /dev/null
+++ b/test cases/common/22 object extraction/check-obj.py	
@@ -0,0 +1,21 @@
+#! /usr/bin/env python3
+
+import json
+import sys
+import os
+
+cc = None
+output = None
+
+# Only the ninja backend produces compile_commands.json
+if sys.argv[1] == 'ninja':
+    with open('compile_commands.json', 'r') as f:
+        cc = json.load(f)
+    output = set((x['output'] for x in cc))
+
+for obj in sys.argv[2:]:
+    if not os.path.exists(obj):
+        sys.exit(1)
+    if sys.argv[1] == 'ninja' and obj not in output:
+        sys.exit(1)
+    print('Verified', obj)
diff --git a/test cases/common/22 object extraction/header.h b/test cases/common/22 object extraction/header.h
new file mode 100644
index 000000000..50403ce3c
--- /dev/null
+++ b/test cases/common/22 object extraction/header.h	
@@ -0,0 +1 @@
+/* Check that extract_all_objects works with headers.  */
diff --git a/test cases/common/22 object extraction/meson.build b/test cases/common/22 object extraction/meson.build
index 18be1dbeb..fd4af8c60 100644
--- a/test cases/common/22 object extraction/meson.build	
+++ b/test cases/common/22 object extraction/meson.build	
@@ -4,20 +4,32 @@ if meson.is_unity()
   message('Skipping extraction test because this is a Unity build.')
 else
   lib1 = shared_library('somelib', 'src/lib.c')
-  lib2 = shared_library('somelib2', 'lib.c', 'lib2.c')
+  lib2 = shared_library('somelib2', 'lib.c', 'header.h', 'lib2.c')
 
   obj1 = lib1.extract_objects('src/lib.c')
   obj2 = lib2.extract_objects(['lib.c'])
   obj3 = lib2.extract_objects(files('lib.c'))
   obj4 = lib2.extract_objects(['lib.c', 'lib.c'])
+  obj5 = lib2.extract_objects(['lib.c', 'header.h'])
+  obj6 = lib2.extract_all_objects(recursive: true)
 
   e1 = executable('main1', 'main.c', objects : obj1)
   e2 = executable('main2', 'main.c', objects : obj2)
   e3 = executable('main3', 'main.c', objects : obj3)
   e4 = executable('main4', 'main.c', objects : obj4)
+  e5 = executable('main5', 'main.c', objects : obj5)
+  e6 = executable('main6', 'main.c', objects : obj6)
+
+  custom_target('custom_target with object inputs', output: 'objs',
+                input: [obj1, obj2, obj3, obj5, obj6],
+                build_by_default: true,
+                command: [find_program('check-obj.py'), meson.backend(), '@INPUT@'],
+                capture: true)
 
   test('extraction test 1', e1)
   test('extraction test 2', e2)
   test('extraction test 3', e3)
   test('extraction test 4', e4)
+  test('extraction test 5', e5)
+  test('extraction test 6', e6)
 endif