diff --git a/src/items/associated-items.md b/src/items/associated-items.md
index dc6c9faef4122..eba9507c7fdfe 100644
--- a/src/items/associated-items.md
+++ b/src/items/associated-items.md
@@ -98,26 +98,28 @@ Associated functions whose first parameter is named `self` are called *methods*
 and may be invoked using the [method call operator], for example, `x.foo()`, as
 well as the usual function call notation.
 
-If the type of the `self` parameter is specified, it is limited to one of the
-following types:
+If the type of the `self` parameter is specified, it is limited to semantic
+types generated by the following grammar (where `'lt` denotes some arbitrary
+lifetime):
 
-- `Self`
-- `&Self`
-- `&mut Self`
-- [`Box<Self>`]
-- [`Rc<Self>`]
-- [`Arc<Self>`]
-- [`Pin<P>`] where `P` is one of the above types except `Self`.
+```text
+P = &'lt S | &'lt mut S | Box<S> | Rc<S> | Arc<S> | Pin<P>
+S = Self | P
+```
 
-The `Self` term can be replaced with the type being implemented, including
-type aliases for the type, or any nested combination of the above types.
+The `Self` terminal in this grammar is the semantic `Self` type and can be
+replaced with the type being implemented, including type aliases or associated
+type projections for the type.
 
 ```rust
 # use std::rc::Rc;
 # use std::sync::Arc;
 # use std::pin::Pin;
+// Examples of methods implemented on struct `Example`.
 struct Example;
 type Alias = Example;
+trait Trait { type Output; }
+impl Trait for Example { type Output = Example; }
 impl Example {
     fn by_value(self: Self) {}
     fn by_ref(self: &Self) {}
@@ -129,6 +131,7 @@ impl Example {
     fn explicit_type(self: Arc<Example>) {}
     fn with_lifetime<'a>(self: &'a Self) {}
     fn nested<'a>(self: &mut &'a Arc<Rc<Box<Alias>>>) {}
+    fn via_projection(self: <Example as Trait>::Output) {}
 }
 ```
 
diff --git a/src/items/traits.md b/src/items/traits.md
index b2132a7e8c697..1a65c9239b6ad 100644
--- a/src/items/traits.md
+++ b/src/items/traits.md
@@ -126,7 +126,7 @@ trait TraitMethods {
 ```
 
 ```rust,compile_fail
-// These are object-safe, but cannot be dispatched on a trait object.
+// This trait is object-safe, but these methods cannot be dispatched on a trait object.
 trait NonDispatchable {
     // Non-methods cannot be dispatched.
     fn foo() where Self: Sized {}
@@ -135,7 +135,6 @@ trait NonDispatchable {
     // `other` may be a different concrete type of the receiver.
     fn param(&self, other: Self) where Self: Sized {}
     // Generics are not compatible with vtables.
-    // Alternate solution is to use a trait object instead.
     fn typed<T>(&self, x: T) where Self: Sized {}
 }
 
@@ -178,7 +177,7 @@ let obj: Box<dyn TraitWithSize> = Box::new(S); // ERROR
 ```
 
 ```rust,compile_fail
-// Not object safe if `Self` is a type parameter.
+// Not object safe if `Self` is a type argument.
 trait Super<A> {}
 trait WithSelf: Super<Self> where Self: Sized {}