diff --git a/src/cmp/cmpopt.lsp b/src/cmp/cmpopt.lsp
index fa904ae90..62fc55902 100644
--- a/src/cmp/cmpopt.lsp
+++ b/src/cmp/cmpopt.lsp
@@ -79,7 +79,7 @@
               when (si::type= type a-type)
               do (return `(,function-name ,object))))
           ;;
-          ;; Complex types defined with DEFTYPE.
+          ;; Derived types defined with DEFTYPE.
           ((and (atom type)
                 (setq function (si:get-sysprop type 'SI::DEFTYPE-DEFINITION)))
            (expand-typep form object `',(funcall function nil) env))
@@ -90,7 +90,7 @@
           ;;
           ;; CONS types. They must be checked _before_ sequence types. We
           ;; do not produce optimized forms because they can be recursive.
-          ((and (consp type) (eq first 'CONS))
+          ((and (consp type) (eq (first type) 'CONS))
            form)
           ;;
           ;; The type denotes a known class and we can check it
@@ -141,13 +141,19 @@
                        (setf ,var2 (truly-the ,first ,var1))
                        (AND ,@(expand-in-interval-p var2 rest)))))))
           ;;
+          ;; Compound COMPLEX types.
+          ((and (eq first 'COMPLEX)
+                (= (list-length type) 2))
+           `(and (typep (realpart ,object) ',(second type))
+                 (typep (imagpart ,object) ',(second type))))
+          ;;
           ;; (SATISFIES predicate)
           ((and (eq first 'SATISFIES)
                 (= (list-length type) 2)
                 (symbolp (setf function (second type))))
            `(,function ,object))
           ;;
-          ;; Complex types with arguments.
+          ;; Derived compound types.
           ((setf function (si:get-sysprop first 'SI::DEFTYPE-DEFINITION))
            (expand-typep form object `',(funcall function rest) env))
           (t
diff --git a/src/lsp/predlib.lsp b/src/lsp/predlib.lsp
index 13be58759..91d3423e3 100644
--- a/src/lsp/predlib.lsp
+++ b/src/lsp/predlib.lsp
@@ -568,9 +568,10 @@ Returns T if X belongs to TYPE; NIL otherwise."
     (COMPLEX
      (and (complexp object)
           (or (null i)
+              ;; type specifier may be i.e (complex integer) so we
+              ;; should check both real and imag part (disregarding
+              ;; the fact that both have the same upgraded type).
               (and (typep (realpart object) (car i))
-                   ;;wfs--should only have to check one.
-                   ;;Illegal to mix real and imaginary types!
                    (typep (imagpart object) (car i))))
            ))
     (SEQUENCE (or (listp object) (vectorp object)))
@@ -1514,9 +1515,17 @@ if not possible."
   (declare (si::c-local))
   (when (eq t1 t2)
     (return-from fast-type= (values t t)))
-  (let* ((tag1 (safe-canonical-type t1))
-         (tag2 (safe-canonical-type t2)))
-    (cond ((and (numberp tag1) (numberp tag2))
+  (let ((tag1 (safe-canonical-type t1))
+        (tag2 (safe-canonical-type t2))
+        (tag3 (safe-canonical-type 'complex)))
+    ;; FAST-TYPE= can't rely on the CANONICAL-TYPE in case of complex
+    ;; numbers which have an exceptional behavior define for TYPEP not
+    ;; being consistent with SUBTYPEP. -- jd 2019-04-19
+    (cond ((and (numberp tag1)
+                (numberp tag2)
+                (/= tag2 tag3))
+           ;; We must call safe-canonical-type again because one of
+           ;; the calls above could have called UPDATE-TYPES.
            (values (= (safe-canonical-type t1) (safe-canonical-type t2))
                    t))
           #+nil