diff --git a/pep-0572.rst b/pep-0572.rst
index b9f58d6f6..3f46ee9e7 100644
--- a/pep-0572.rst
+++ b/pep-0572.rst
@@ -111,8 +111,6 @@ efficient rewrite would have been::
         if match2:
             return match2.group(2)
 
-(TODO: Include Guido's evidence, and do a more systematic search.)
-
 
 Syntax and semantics
 ====================
@@ -144,50 +142,45 @@ There are a few places where assignment expressions are not allowed,
 in order to avoid ambiguities or user confusion:
 
 - Unparenthesized assignment expressions are prohibited at the top
-  level of an expression statement; for example, this is not allowed::
+  level of an expression statement.  Example::
 
     y := f(x)  # INVALID
+    (y := f(x))  # Valid, though not recommended
 
   This rule is included to simplify the choice for the user between an
   assignment statements and an assignment expression -- there is no
   syntactic position where both are valid.
 
 - Unparenthesized assignment expressions are prohibited at the top
-  level in the right hand side of an assignment statement; for
-  example, the following is not allowed::
+  level of the right hand side of an assignment statement.  Example::
 
     y0 = y1 := f(x)  # INVALID
+    y0 = (y1 := f(x))  # Valid, though discouraged
 
   Again, this rule is included to avoid two visually similar ways of
   saying the same thing.
 
 - Unparenthesized assignment expressions are prohibited for the value
-  of a keyword argument in a call; for example, this is disallowed::
+  of a keyword argument in a call.  Example::
 
     foo(x = y := f(x))  # INVALID
+    foo(x=(y := f(x)))  # Valid, though probably confusing
 
   This rule is included to disallow excessively confusing code, and
   because parsing keyword arguments is complex enough already.
 
-- Assignment expressions (even parenthesized or occurring inside other
-  constructs) are prohibited in function default values.  For example,
-  the following examples are all invalid, even though the expressions
-  for the default values are valid in other contexts::
+- Unparenthesized assignment expressions are prohibited at the top
+  level of a function default value.  Example::
 
     def foo(answer = p := 42):  # INVALID
         ...
-
-    def bar(answer = (p := 42)):  # INVALID
+    def foo(answer=(p := 42)):  # Valid, though not great style
         ...
 
-    def baz(callback = (lambda arg: p := arg)):  # INVALID
-        ...
-
-  This rule is included to avoid side effects in a position whose
+  This rule is included to discourage side effects in a position whose
   exact semantics are already confusing to many users (cf. the common
-  style recommendation against mutable default values).  (TODO: Maybe
-  this should just be a style recommendation except for the
-  prohibition at the top level?)
+  style recommendation against mutable default values), and also to
+  echo the similar prohibition in calls (the previous bullet).
 
 Scope of the target
 -------------------
@@ -196,7 +189,8 @@ An assignment expression does not introduce a new scope.  In most
 cases the scope in which the target will be bound is self-explanatory:
 it is the current scope.  If this scope contains a ``nonlocal`` or
 ``global`` declaration for the target, the assignment expression
-honors that.
+honors that.  A lambda (being an explicit, if anonymous, function
+definition) counts as a scope for this purpose.
 
 There is one special case: an assignment expression occurring in a
 list, set or dict comprehension or in a generator expression (below
@@ -231,12 +225,11 @@ comprehension, for example::
 
 An exception to this special case applies when the target name is the
 same as a loop control variable for a comprehension containing it.
-This is invalid.  (This exception exists to rule out edge cases of the
+This is invalid.  This exception exists to rule out edge cases of the
 above scope rules as illustrated by ``[i := i+1 for i in range(5)]``
 or ``[[(j := j) for i in range(5)] for j in range(5)]``.  Note that
-this exception also applies to ``[i := 0 for i, j in stuff]``.)
-
-TODO: prohibit [... for i in i := ...]
+this exception also applies to ``[i := 0 for i, j in stuff]``, as well
+as to cases like ``[i+1 for i in i := stuff]``.
 
 A further exception applies when an assignment expression occurrs in a
 comprehension whose containing scope is a class scope.  If the rules
@@ -254,7 +247,8 @@ variable defined in the class scope from a comprehension.)
 See Appendix B for some examples of how the rules for targets in
 comprehensions translate to equivalent code.
 
-TODO: use a a subclass of SyntaxError for various prohibitions?
+The two invalid cases listed above raise ``TargetScopeError``, a
+subclass of ``SyntaxError`` (with the same signature).
 
 Relative precedence of ``:=``
 -----------------------------