diff --git a/docs/source/error_code_list.rst b/docs/source/error_code_list.rst
index 1f75ac54d525..a865a4dd1532 100644
--- a/docs/source/error_code_list.rst
+++ b/docs/source/error_code_list.rst
@@ -741,7 +741,7 @@ returns ``None``:
    # OK: we don't do anything with the return value
    f()
 
-   # Error: "f" does not return a value  [func-returns-value]
+   # Error: "f" does not return a value (it only ever returns None)  [func-returns-value]
    if f():
         print("not false")
 
diff --git a/mypy/messages.py b/mypy/messages.py
index cda4cda25ee4..4b71bd876dcc 100644
--- a/mypy/messages.py
+++ b/mypy/messages.py
@@ -1021,18 +1021,11 @@ def duplicate_argument_value(self, callee: CallableType, index: int, context: Co
 
     def does_not_return_value(self, callee_type: Type | None, context: Context) -> None:
         """Report an error about use of an unusable type."""
-        name: str | None = None
         callee_type = get_proper_type(callee_type)
-        if isinstance(callee_type, FunctionLike):
-            name = callable_name(callee_type)
-        if name is not None:
-            self.fail(
-                f"{capitalize(name)} does not return a value",
-                context,
-                code=codes.FUNC_RETURNS_VALUE,
-            )
-        else:
-            self.fail("Function does not return a value", context, code=codes.FUNC_RETURNS_VALUE)
+        callee_name = callable_name(callee_type) if isinstance(callee_type, FunctionLike) else None
+        name = callee_name or "Function"
+        message = f"{name} does not return a value (it only ever returns None)"
+        self.fail(message, context, code=codes.FUNC_RETURNS_VALUE)
 
     def deleted_as_rvalue(self, typ: DeletedType, context: Context) -> None:
         """Report an error about using an deleted type as an rvalue."""
diff --git a/test-data/unit/check-errorcodes.test b/test-data/unit/check-errorcodes.test
index 796e1c1ea98e..df14e328ed72 100644
--- a/test-data/unit/check-errorcodes.test
+++ b/test-data/unit/check-errorcodes.test
@@ -553,15 +553,15 @@ from typing import Callable
 
 def f() -> None: pass
 
-x = f()  # E: "f" does not return a value  [func-returns-value]
+x = f()  # E: "f" does not return a value (it only ever returns None)  [func-returns-value]
 
 class A:
     def g(self) -> None: pass
 
-y = A().g()  # E: "g" of "A" does not return a value  [func-returns-value]
+y = A().g()  # E: "g" of "A" does not return a value (it only ever returns None)  [func-returns-value]
 
 c: Callable[[], None]
-z = c()  # E: Function does not return a value  [func-returns-value]
+z = c()  # E: Function does not return a value (it only ever returns None)  [func-returns-value]
 
 [case testErrorCodeInstantiateAbstract]
 from abc import abstractmethod
diff --git a/test-data/unit/check-expressions.test b/test-data/unit/check-expressions.test
index c213255997f8..a3c1bc8795f2 100644
--- a/test-data/unit/check-expressions.test
+++ b/test-data/unit/check-expressions.test
@@ -1079,15 +1079,15 @@ class A:
 a: A
 o: object
 if int():
-    a = f()         # E: "f" does not return a value
+    a = f()         # E: "f" does not return a value (it only ever returns None)
 if int():
-    o = a()         # E: Function does not return a value
+    o = a()         # E: Function does not return a value (it only ever returns None)
 if int():
-    o = A().g(a)    # E: "g" of "A" does not return a value
+    o = A().g(a)    # E: "g" of "A" does not return a value (it only ever returns None)
 if int():
-    o = A.g(a, a)   # E: "g" of "A" does not return a value
-A().g(f())      # E: "f" does not return a value
-x: A = f()      # E: "f" does not return a value
+    o = A.g(a, a)   # E: "g" of "A" does not return a value (it only ever returns None)
+A().g(f())      # E: "f" does not return a value (it only ever returns None)
+x: A = f()      # E: "f" does not return a value (it only ever returns None)
 f()
 A().g(a)
 [builtins fixtures/tuple.pyi]
@@ -1096,15 +1096,15 @@ A().g(a)
 import typing
 def f() -> None: pass
 
-if f():   # E: "f" does not return a value
+if f():   # E: "f" does not return a value (it only ever returns None)
     pass
-elif f(): # E: "f" does not return a value
+elif f(): # E: "f" does not return a value (it only ever returns None)
     pass
-while f(): # E: "f" does not return a value
+while f(): # E: "f" does not return a value (it only ever returns None)
     pass
 def g() -> object:
-    return f() # E: "f" does not return a value
-raise f() # E: "f" does not return a value
+    return f() # E: "f" does not return a value (it only ever returns None)
+raise f() # E: "f" does not return a value (it only ever returns None)
 [builtins fixtures/exception.pyi]
 
 [case testNoneReturnTypeWithExpressions]
@@ -1115,13 +1115,13 @@ class A:
     def __add__(self, x: 'A') -> 'A': pass
 
 a: A
-[f()]       # E: "f" does not return a value
-f() + a     # E: "f" does not return a value
-a + f()     # E: "f" does not return a value
-f() == a    # E: "f" does not return a value
-a != f()    # E: "f" does not return a value
+[f()]       # E: "f" does not return a value (it only ever returns None)
+f() + a     # E: "f" does not return a value (it only ever returns None)
+a + f()     # E: "f" does not return a value (it only ever returns None)
+f() == a    # E: "f" does not return a value (it only ever returns None)
+a != f()    # E: "f" does not return a value (it only ever returns None)
 cast(A, f())
-f().foo     # E: "f" does not return a value
+f().foo     # E: "f" does not return a value (it only ever returns None)
 [builtins fixtures/list.pyi]
 
 [case testNoneReturnTypeWithExpressions2]
@@ -1134,14 +1134,14 @@ class A:
 
 a: A
 b: bool
-f() in a   # E: "f" does not return a value  # E: Unsupported right operand type for in ("A")
-a < f()    # E: "f" does not return a value
-f() <= a   # E: "f" does not return a value
-a in f()   # E: "f" does not return a value
--f()       # E: "f" does not return a value
-not f()    # E: "f" does not return a value
-f() and b  # E: "f" does not return a value
-b or f()   # E: "f" does not return a value
+f() in a   # E: "f" does not return a value (it only ever returns None)  # E: Unsupported right operand type for in ("A")
+a < f()    # E: "f" does not return a value (it only ever returns None)
+f() <= a   # E: "f" does not return a value (it only ever returns None)
+a in f()   # E: "f" does not return a value (it only ever returns None)
+-f()       # E: "f" does not return a value (it only ever returns None)
+not f()    # E: "f" does not return a value (it only ever returns None)
+f() and b  # E: "f" does not return a value (it only ever returns None)
+b or f()   # E: "f" does not return a value (it only ever returns None)
 [builtins fixtures/bool.pyi]
 
 
@@ -1441,7 +1441,7 @@ if int():
 [case testConditionalExpressionWithEmptyCondition]
 import typing
 def f() -> None: pass
-x = 1 if f() else 2 # E: "f" does not return a value
+x = 1 if f() else 2 # E: "f" does not return a value (it only ever returns None)
 
 [case testConditionalExpressionWithSubtyping]
 import typing
@@ -1504,7 +1504,7 @@ from typing import List, Union
 x = []
 y = ""
 x.append(y) if bool() else x.append(y)
-z = x.append(y) if bool() else x.append(y) # E: "append" of "list" does not return a value
+z = x.append(y) if bool() else x.append(y) # E: "append" of "list" does not return a value (it only ever returns None)
 [builtins fixtures/list.pyi]
 
 -- Special cases
@@ -1604,7 +1604,7 @@ def f(x: int) -> None:
 [builtins fixtures/for.pyi]
 [out]
 main:1: error: The return type of a generator function should be "Generator" or one of its supertypes
-main:2: error: "f" does not return a value
+main:2: error: "f" does not return a value (it only ever returns None)
 main:2: error: Argument 1 to "f" has incompatible type "str"; expected "int"
 
 [case testYieldExpressionWithNone]
@@ -1624,7 +1624,7 @@ from typing import Iterator
 def f() -> Iterator[int]:
     yield 5
 def g() -> Iterator[int]:
-    a = yield from f()  # E: Function does not return a value
+    a = yield from f()  # E: Function does not return a value (it only ever returns None)
 
 [case testYieldFromGeneratorHasValue]
 from typing import Iterator, Generator
@@ -1639,12 +1639,12 @@ def g() -> Iterator[int]:
 [case testYieldFromTupleExpression]
 from typing import Generator
 def g() -> Generator[int, None, None]:
-    x = yield from ()  # E: Function does not return a value
-    x = yield from (0, 1, 2)  # E: Function does not return a value
+    x = yield from ()  # E: Function does not return a value (it only ever returns None)
+    x = yield from (0, 1, 2)  # E: Function does not return a value (it only ever returns None)
     x = yield from (0, "ERROR")  # E: Incompatible types in "yield from" (actual type "object", expected type "int") \
-                                 # E: Function does not return a value
+                                 # E: Function does not return a value (it only ever returns None)
     x = yield from ("ERROR",)  # E: Incompatible types in "yield from" (actual type "str", expected type "int") \
-                               # E: Function does not return a value
+                               # E: Function does not return a value (it only ever returns None)
 [builtins fixtures/tuple.pyi]
 
 -- dict(...)
diff --git a/test-data/unit/check-functions.test b/test-data/unit/check-functions.test
index 4cc523a595d1..cd098a84d4d3 100644
--- a/test-data/unit/check-functions.test
+++ b/test-data/unit/check-functions.test
@@ -250,7 +250,7 @@ if int():
 if int():
     f = o   # E: Incompatible types in assignment (expression has type "object", variable has type "Callable[[], None]")
 if int():
-    f = f() # E: Function does not return a value
+    f = f() # E: Function does not return a value (it only ever returns None)
 
 if int():
     f = f
diff --git a/test-data/unit/check-inference.test b/test-data/unit/check-inference.test
index 36b028977591..f9a4d58c74af 100644
--- a/test-data/unit/check-inference.test
+++ b/test-data/unit/check-inference.test
@@ -33,8 +33,8 @@ class B: pass
 [case testLvarInitializedToVoid]
 import typing
 def f() -> None:
-    a = g()    # E: "g" does not return a value
-    #b, c = g() # "g" does not return a value TODO
+    a = g()    # E: "g" does not return a value (it only ever returns None)
+    #b, c = g() # "g" does not return a value (it only ever returns None) TODO
 
 def g() -> None: pass
 [out]
@@ -1180,7 +1180,7 @@ for e, f in [[]]:  # E: Need type annotation for "e" \
 [case testForStatementInferenceWithVoid]
 def f() -> None: pass
 
-for x in f(): # E: "f" does not return a value
+for x in f(): # E: "f" does not return a value (it only ever returns None)
     pass
 [builtins fixtures/for.pyi]
 
@@ -2118,7 +2118,7 @@ arr = []
 arr.append(arr.append(1))
 [builtins fixtures/list.pyi]
 [out]
-main:3: error: "append" of "list" does not return a value
+main:3: error: "append" of "list" does not return a value (it only ever returns None)
 
 -- Multipass
 -- ---------
diff --git a/test-data/unit/check-optional.test b/test-data/unit/check-optional.test
index ae247b0047f1..70f3c4486e14 100644
--- a/test-data/unit/check-optional.test
+++ b/test-data/unit/check-optional.test
@@ -361,9 +361,9 @@ def f() -> None:
 def g(x: Optional[int]) -> int:
   pass
 
-x = f()  # E: "f" does not return a value
-f() + 1  # E: "f" does not return a value
-g(f())  # E: "f" does not return a value
+x = f()  # E: "f" does not return a value (it only ever returns None)
+f() + 1  # E: "f" does not return a value (it only ever returns None)
+g(f())  # E: "f" does not return a value (it only ever returns None)
 
 [case testEmptyReturn]
 def f() -> None:
diff --git a/test-data/unit/check-tuples.test b/test-data/unit/check-tuples.test
index cff261774663..0e7c81edc498 100644
--- a/test-data/unit/check-tuples.test
+++ b/test-data/unit/check-tuples.test
@@ -169,8 +169,8 @@ class C(B): pass
 import typing
 def f() -> None: pass
 
-(None, f()) # E: "f" does not return a value
-(f(), None) # E: "f" does not return a value
+(None, f()) # E: "f" does not return a value (it only ever returns None)
+(f(), None) # E: "f" does not return a value (it only ever returns None)
 [builtins fixtures/tuple.pyi]
 
 
diff --git a/test-data/unit/check-varargs.test b/test-data/unit/check-varargs.test
index 54546f3973b3..ef2c3c57fad5 100644
--- a/test-data/unit/check-varargs.test
+++ b/test-data/unit/check-varargs.test
@@ -52,8 +52,8 @@ c: C
 
 f(c)       # E: Argument 1 to "f" has incompatible type "C"; expected "A"
 f(a, b, c) # E: Argument 3 to "f" has incompatible type "C"; expected "A"
-f(g())     # E: "g" does not return a value
-f(a, g())  # E: "g" does not return a value
+f(g())     # E: "g" does not return a value (it only ever returns None)
+f(a, g())  # E: "g" does not return a value (it only ever returns None)
 f()
 f(a)
 f(b)
diff --git a/test-data/unit/pythoneval-asyncio.test b/test-data/unit/pythoneval-asyncio.test
index 069374b9635c..4a185557495b 100644
--- a/test-data/unit/pythoneval-asyncio.test
+++ b/test-data/unit/pythoneval-asyncio.test
@@ -261,7 +261,7 @@ try:
 finally:
     loop.close()
 [out]
-_program.py:11: error: Function does not return a value
+_program.py:11: error: Function does not return a value (it only ever returns None)
 
 [case testErrorReturnIsNotTheSameType]
 from typing import Any