diff --git a/src/cmd/cgo/gcc.go b/src/cmd/cgo/gcc.go
index eb6c1a5..730db44 100644
--- a/src/cmd/cgo/gcc.go
+++ b/src/cmd/cgo/gcc.go
@@ -2448,6 +2448,18 @@
 			tt := *t
 			tt.C = &TypeRepr{"%s %s", []interface{}{dt.Kind, tag}}
 			tt.Go = c.Ident("struct{}")
+			if dt.Kind == "struct" {
+				// We don't know what the representation of this struct is, so don't let
+				// anyone allocate one on the Go side. As a side effect of this annotation,
+				// pointers to this type will not be considered pointers in Go. They won't
+				// get writebarrier-ed or adjusted during a stack copy. This should handle
+				// all the cases badPointerTypedef used to handle, but hopefully will
+				// continue to work going forward without any more need for cgo changes.
+				tt.NotInHeap = true
+				// TODO: we should probably do the same for unions. Unions can't live
+				// on the Go heap, right? It currently doesn't work for unions because
+				// they are defined as a type alias for struct{}, not a defined type.
+			}
 			typedef[name.Name] = &tt
 			break
 		}
@@ -2518,6 +2530,7 @@
 		}
 		t.Go = name
 		t.BadPointer = sub.BadPointer
+		t.NotInHeap = sub.NotInHeap
 		if unionWithPointer[sub.Go] {
 			unionWithPointer[t.Go] = true
 		}
@@ -2528,6 +2541,7 @@
 			tt := *t
 			tt.Go = sub.Go
 			tt.BadPointer = sub.BadPointer
+			tt.NotInHeap = sub.NotInHeap
 			typedef[name.Name] = &tt
 		}
 
@@ -3026,6 +3040,7 @@
 // non-pointers in this type.
 // TODO: Currently our best solution is to find these manually and list them as
 // they come up. A better solution is desired.
+// Note: DEPRECATED. There is now a better solution. Search for NotInHeap in this file.
 func (c *typeConv) badPointerTypedef(dt *dwarf.TypedefType) bool {
 	if c.badCFType(dt) {
 		return true
diff --git a/src/cmd/cgo/main.go b/src/cmd/cgo/main.go
index 5a7bb3f..ef3ed96 100644
--- a/src/cmd/cgo/main.go
+++ b/src/cmd/cgo/main.go
@@ -151,7 +151,8 @@
 	Go         ast.Expr
 	EnumValues map[string]int64
 	Typedef    string
-	BadPointer bool
+	BadPointer bool // this pointer type should be represented as a uintptr (deprecated)
+	NotInHeap  bool // this type should have a go:notinheap annotation
 }
 
 // A FuncType collects information about a function type in both the C and Go worlds.
diff --git a/src/cmd/cgo/out.go b/src/cmd/cgo/out.go
index 50d2811..03b8333 100644
--- a/src/cmd/cgo/out.go
+++ b/src/cmd/cgo/out.go
@@ -108,6 +108,9 @@
 	sort.Strings(typedefNames)
 	for _, name := range typedefNames {
 		def := typedef[name]
+		if def.NotInHeap {
+			fmt.Fprintf(fgo2, "//go:notinheap\n")
+		}
 		fmt.Fprintf(fgo2, "type %s ", name)
 		// We don't have source info for these types, so write them out without source info.
 		// Otherwise types would look like:
diff --git a/test/fixedbugs/issue40954.go b/test/fixedbugs/issue40954.go
new file mode 100644
index 0000000..53e9ccf
--- /dev/null
+++ b/test/fixedbugs/issue40954.go
@@ -0,0 +1,35 @@
+// run
+
+// Copyright 2020 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package main
+
+import (
+	"unsafe"
+)
+
+//go:notinheap
+type S struct{ x int }
+
+func main() {
+	var i int
+	p := (*S)(unsafe.Pointer(uintptr(unsafe.Pointer(&i))))
+	v := uintptr(unsafe.Pointer(p))
+	// p is a pointer to a go:notinheap type. Like some C libraries,
+	// we stored an integer in that pointer. That integer just happens
+	// to be the address of i.
+	// v is also the address of i.
+	// p has a base type which is marked go:notinheap, so it
+	// should not be adjusted when the stack is copied.
+	recurse(100, p, v)
+}
+func recurse(n int, p *S, v uintptr) {
+	if n > 0 {
+		recurse(n-1, p, v)
+	}
+	if uintptr(unsafe.Pointer(p)) != v {
+		panic("adjusted notinheap pointer")
+	}
+}