diff --git a/src/cmd/compile/internal/types2/stmt.go b/src/cmd/compile/internal/types2/stmt.go
index e826f35105d..10741a90e2e 100644
--- a/src/cmd/compile/internal/types2/stmt.go
+++ b/src/cmd/compile/internal/types2/stmt.go
@@ -834,19 +834,28 @@ func (check *Checker) rangeStmt(inner stmtContext, s *syntax.ForStmt, rclause *s
 	// determine key/value types
 	var key, val Type
 	if x.mode != invalid {
-		// Ranging over a type parameter is permitted if it has a structural type.
-		typ := optype(x.typ)
-		if _, ok := typ.(*Chan); ok && sValue != nil {
-			check.softErrorf(sValue, "range over %s permits only one iteration variable", &x)
-			// ok to continue
-		}
-		var msg string
-		key, val, msg = rangeKeyVal(typ, isVarName(sKey), isVarName(sValue))
-		if key == nil || msg != "" {
-			if msg != "" {
-				msg = ": " + msg
+		// Ranging over a type parameter is permitted if it has a single underlying type.
+		var cause string
+		u := singleUnder(x.typ)
+		switch t := u.(type) {
+		case nil:
+			cause = "type set has no single underlying type"
+		case *Chan:
+			if sValue != nil {
+				check.softErrorf(sValue, "range over %s permits only one iteration variable", &x)
+				// ok to continue
+			}
+			if t.dir == SendOnly {
+				cause = "receive from send-only channel"
+			}
+		}
+		key, val = rangeKeyVal(u)
+		if key == nil || cause != "" {
+			if cause == "" {
+				check.softErrorf(&x, "cannot range over %s", &x)
+			} else {
+				check.softErrorf(&x, "cannot range over %s (%s)", &x, cause)
 			}
-			check.softErrorf(&x, "cannot range over %s%s", &x, msg)
 			// ok to continue
 		}
 	}
@@ -927,44 +936,23 @@ func (check *Checker) rangeStmt(inner stmtContext, s *syntax.ForStmt, rclause *s
 	check.stmt(inner, s.Body)
 }
 
-// isVarName reports whether x is a non-nil, non-blank (_) expression.
-func isVarName(x syntax.Expr) bool {
-	if x == nil {
-		return false
-	}
-	ident, _ := unparen(x).(*syntax.Name)
-	return ident == nil || ident.Value != "_"
-}
-
 // rangeKeyVal returns the key and value type produced by a range clause
-// over an expression of type typ, and possibly an error message. If the
-// range clause is not permitted the returned key is nil or msg is not
-// empty (in that case we still may have a non-nil key type which can be
-// used to reduce the chance for follow-on errors).
-// The wantKey, wantVal, and hasVal flags indicate which of the iteration
-// variables are used or present; this matters if we range over a generic
-// type where not all keys or values are of the same type.
-func rangeKeyVal(typ Type, wantKey, wantVal bool) (Type, Type, string) {
+// over an expression of type typ. If the range clause is not permitted
+// the results are nil.
+func rangeKeyVal(typ Type) (key, val Type) {
 	switch typ := arrayPtrDeref(typ).(type) {
 	case *Basic:
 		if isString(typ) {
-			return Typ[Int], universeRune, "" // use 'rune' name
+			return Typ[Int], universeRune // use 'rune' name
 		}
 	case *Array:
-		return Typ[Int], typ.elem, ""
+		return Typ[Int], typ.elem
 	case *Slice:
-		return Typ[Int], typ.elem, ""
+		return Typ[Int], typ.elem
 	case *Map:
-		return typ.key, typ.elem, ""
+		return typ.key, typ.elem
 	case *Chan:
-		var msg string
-		if typ.dir == SendOnly {
-			msg = "receive from send-only channel"
-		}
-		return typ.elem, Typ[Invalid], msg
-	case *top:
-		// we have a type parameter with no structural type
-		return nil, nil, "no structural type"
+		return typ.elem, Typ[Invalid]
 	}
-	return nil, nil, ""
+	return
 }
diff --git a/src/cmd/compile/internal/types2/testdata/check/typeparams.go2 b/src/cmd/compile/internal/types2/testdata/check/typeparams.go2
index 29c25b0bb48..d1f07a20d4f 100644
--- a/src/cmd/compile/internal/types2/testdata/check/typeparams.go2
+++ b/src/cmd/compile/internal/types2/testdata/check/typeparams.go2
@@ -184,7 +184,7 @@ func _[
         for _, _ = range b1 {}
 
         var b2 B2
-        for range b2 /* ERROR cannot range over b2 .* no structural type */ {}
+        for range b2 {}
 
         var c0 chan int
         for range c0 {}
@@ -197,7 +197,7 @@ func _[
         for _, _ /* ERROR permits only one iteration variable */ = range c1 {}
 
         var c2 C2
-        for range c2 /* ERROR cannot range over c2 .* no structural type */ {}
+        for range c2 /* ERROR cannot range over c2.*no single underlying type */ {}
 
         var c3 C3
         for range c3 /* ERROR receive from send-only channel */ {}
@@ -213,7 +213,7 @@ func _[
         for _, _ = range s1 {}
 
         var s2 S2
-        for range s2 /* ERROR cannot range over s2 .* no structural type */ {}
+        for range s2 /* ERROR cannot range over s2.*no single underlying type */ {}
 
         var a0 []int
         for range a0 {}
@@ -226,7 +226,7 @@ func _[
         for _, _ = range a1 {}
 
         var a2 A2
-        for range a2 /* ERROR cannot range over a2 .* no structural type */ {}
+        for range a2 /* ERROR cannot range over a2.*no single underlying type */ {}
 
         var p0 *[10]int
         for range p0 {}
@@ -239,7 +239,7 @@ func _[
         for _, _ = range p1 {}
 
         var p2 P2
-        for range p2 /* ERROR cannot range over p2 .* no structural type */ {}
+        for range p2 /* ERROR cannot range over p2.*no single underlying type */ {}
 
         var m0 map[string]int
         for range m0 {}
@@ -252,7 +252,7 @@ func _[
         for _, _ = range m1 {}
 
         var m2 M2
-        for range m2 /* ERROR cannot range over m2 .* no structural type */ {}
+        for range m2 /* ERROR cannot range over m2.*no single underlying type */ {}
 }
 
 // type inference checks