diff --git a/s/cptypes.ss b/s/cptypes.ss
index f08867cda2..73954d1a8d 100644
--- a/s/cptypes.ss
+++ b/s/cptypes.ss
@@ -1033,6 +1033,57 @@ Notes:
                  [else
                   (values `(call ,preinfo ,pr ,n) ret ntypes #f #f)]))])
 
+      (define-specialize 2 atan
+        [(n) (let ([r (get-type n)])
+               (cond
+                 [(predicate-implies-not? r 'number)
+                  (values `(call ,preinfo ,pr ,n)
+                          'bottom pred-env-bottom #f #f)]
+                 [else
+                  (values `(call ,preinfo ,pr ,n) ret 
+                          (pred-env-add/ref ntypes n 'number plxc) #f #f)]))]
+        [(x y) (let ([rx (get-type x)]
+                     [ry (get-type y)])
+                 (cond
+                   [(or (predicate-implies-not? rx 'real)
+                        (predicate-implies-not? ry 'real))
+                    (values `(call ,preinfo ,pr ,x ,y)
+                            'bottom pred-env-bottom #f #f)]
+                   [else
+                    (values `(call ,preinfo ,pr ,x ,y) ret 
+                            (pred-env-add/ref (pred-env-add/ref ntypes
+                                                                x 'real  plxc)
+                                              y 'real plxc)
+                             #f #f)]))])
+
+      (define-specialize 2 char-name
+        [(n) (let ([r (get-type n)]
+                   [ir `(call ,preinfo ,pr ,n)])
+               (cond
+                 [(predicate-implies? r 'char)
+                  (values ir 'ptr ntypes #f #f)] ; should be maybe-symbol
+                 [(predicate-implies? r 'symbol)
+                  (values ir 'ptr ntypes #f #f)] ; should be maybe-char
+                 [(and (predicate-implies-not? r 'char)
+                       (predicate-implies-not? r 'symbol))
+                  (values ir 'bottom pred-env-bottom #f #f)]
+                 [else
+                  (values ir 'ptr                                            ; should be maybe-(union 'char 'symbol)
+                          (pred-env-add/ref ntypes n 'true  plxc) #f #f)]))] ; should be (union 'char 'symbol)
+        [(n c) (let ([rn (get-type n)]
+                     [rc (get-type c)]
+                     [ir `(call ,preinfo ,pr ,n ,c)])
+                 (cond
+                   [(or (predicate-implies-not? rn 'symbol)
+                        (predicate-implies-not? rc 'ptr)) ; should be maybe-char
+                    (values ir 'bottom pred-env-bottom #f #f)]
+                   [else
+                    (values ir void-rec
+                            (pred-env-add/ref (pred-env-add/ref ntypes
+                                                                n 'symbol plxc)
+                                              c 'ptr plxc) ; should be maybe-char
+                             #f #f)]))])
+
       (define-specialize/unrestricted 2 call-with-values
         [(e1 e2) (let-values ([(e1 ret1 types1 t-types1 f-types1)
                                (Expr/call e1 'value oldtypes oldtypes plxc)])
diff --git a/s/primdata.ss b/s/primdata.ss
index 4861035d14..9c1d06d7f3 100644
--- a/s/primdata.ss
+++ b/s/primdata.ss
@@ -238,7 +238,7 @@
   (tan [sig [(number) -> (number)]] [flags arith-op mifoldable discard ieee r5rs])
   (asin [sig [(number) -> (number)]] [flags arith-op mifoldable discard ieee r5rs])
   (acos [sig [(number) -> (number)]] [flags arith-op mifoldable discard ieee r5rs])
-  (atan [sig [(number) (real real) -> (number)]] [flags arith-op mifoldable discard ieee r5rs])
+  (atan [sig [(number) (real real) -> (number)]] [flags arith-op mifoldable discard cptypes2 ieee r5rs])
   (sqrt [sig [(number) -> (number)]] [flags arith-op mifoldable discard ieee r5rs])
   (exact-integer-sqrt [sig [(exact-integer) -> (exact-integer exact-integer)]] [flags discard discard]) ; could be mifoldable if multiple values were handled
   (expt [sig [(number number) -> (number)]] [flags pure discard true cp02 ieee r5rs]) ; can take too long to fold
@@ -1215,7 +1215,7 @@
   (char-ci=? [sig [(char char ...) -> (boolean)]] [flags pure mifoldable discard cp03 safeongoodargs])   ; not restricted to 2+ arguments
   (char-ci>=? [sig [(char char ...) -> (boolean)]] [flags pure mifoldable discard safeongoodargs])  ; not restricted to 2+ arguments
   (char-ci>? [sig [(char char ...) -> (boolean)]] [flags pure mifoldable discard safeongoodargs])   ; not restricted to 2+ arguments
-  (char-name [sig [(sub-ptr) (sub-symbol maybe-char) -> (ptr)]] [flags])
+  (char-name [sig [(sub-ptr) (sub-symbol maybe-char) -> (ptr)]] [flags cptypes2])
   (char-ready? [sig [() (textual-input-port) -> (boolean)]] [flags ieee r5rs])
   (chmod [sig [(pathname sub-ufixnum) -> (void)]] [flags])
   (clear-input-port [sig [() (input-port) -> (void)]] [flags true])