diff --git a/typed-racket-lib/typed-racket/infer/infer-unit.rkt b/typed-racket-lib/typed-racket/infer/infer-unit.rkt
index da1db939b..86d112655 100644
--- a/typed-racket-lib/typed-racket/infer/infer-unit.rkt
+++ b/typed-racket-lib/typed-racket/infer/infer-unit.rkt
@@ -22,6 +22,7 @@
          "signatures.rkt" "fail.rkt"
          "promote-demote.rkt"
          racket/match
+         (only-in racket/function curry curryr thunk)
          ;racket/trace
          (contract-req)
          (for-syntax
@@ -38,6 +39,7 @@
 (define (empty-set) '())
 
 (define current-seen (make-parameter (empty-set)))
+(define infered-tvar-map (make-parameter (hash)))
 
 ;; Type Type -> Pair<Seq, Seq>
 ;; construct a pair for the set of seen type pairs
@@ -65,6 +67,7 @@
     [(context V X Y)
      (context (append bounds V) (append vars X) (append indices Y))]))
 
+
 (define (inferable-index? ctx bound)
   (match ctx
     [(context _ _ Y)
@@ -492,6 +495,31 @@
   ;; this constrains just x (which is a single var)
   (define (singleton S x T)
     (insert empty x S T))
+
+  (define (constrain tvar-a tvar-b #:above above)
+    (define (maybe-type-app t)
+      (match t
+        [(App: t1 (list (F: var))) #:when (hash-has-key? (infered-tvar-map) var)
+                                   (define v (hash-ref (infered-tvar-map) var))
+                                   (-App t1 (list v))]
+        [_ t]))
+
+    (match-define (F: var (app maybe-type-app maybe-type-bound)) tvar-a)
+
+    (define-values (default sub sing) (if above
+                                          (values Univ
+                                                  (thunk (subtype tvar-b maybe-type-bound obj))
+                                                  (curry singleton (var-promote tvar-b (context-bounds context)) var))
+                                          (values -Bottom
+                                                  (thunk (subtype maybe-type-bound tvar-b obj))
+                                                  (curryr singleton var (var-demote tvar-b (context-bounds context))))))
+    (cond
+      [(not maybe-type-bound) (sing default)]
+      [(sub)
+       (infered-tvar-map (hash-set (infered-tvar-map) var maybe-type-bound))
+       (sing maybe-type-bound)]
+      [else #f]))
+
   ;; FIXME -- figure out how to use parameters less here
   ;;          subtyping doesn't need to use it quite as much
   (define cs (current-seen))
@@ -568,24 +596,24 @@
 
         ;; variables that are in X and should be constrained
         ;; all other variables are compatible only with themselves
-        [((F: (? (inferable-var? context) v)) T)
+        [((F: (? (inferable-var? context))) T)
          #:return-when
          (match T
            ;; fail when v* is an index variable
            [(F: v*) (and (bound-index? v*) (not (bound-tvar? v*)))]
            [_ #f])
          #f
-         ;; constrain v to be below T (but don't mention bounds)
-         (singleton -Bottom v (var-demote T (context-bounds context)))]
+         ;; constrain S to be below T (but don't mention bounds)
+         (constrain S T #:above #f)]
 
-        [(S (F: (? (inferable-var? context) v)))
+        [(S (F: (? (inferable-var? context))))
          #:return-when
          (match S
            [(F: v*) (and (bound-index? v*) (not (bound-tvar? v*)))]
            [_ #f])
          #f
-         ;; constrain v to be above S (but don't mention bounds)
-         (singleton (var-promote S (context-bounds context)) v Univ)]
+         ;; constrain T to be above S (but don't mention bounds)
+         (constrain T S #:above #t)]
 
         ;; recursive names should get resolved as they're seen
         [(s (? Name? t))
@@ -595,6 +623,10 @@
          (let ([s (resolve-once s)])
            (and s (cg s t obj)))]
 
+        [((F: var (? Type? bound)) t)
+         (let ([s (resolve-once bound)])
+           (and s (cg s t obj)))]
+
         ;; constrain b1 to be below T, but don't mention the new vars
         [((Poly: v1 b1) T) (cgen (context-add context #:bounds v1) b1 T)]
 
@@ -966,6 +998,7 @@
         (build-subst md))
       (build-subst (stream-first (cset-maps C)))))
 
+
 ;; context : the context of what to infer/not infer
 ;; S : a list of types to be the subtypes of T
 ;; T : a list of types
@@ -983,9 +1016,9 @@
           (for/list/fail ([s (in-list S)]
                           [t (in-list T)]
                           [obj (in-list/rest objs #f)])
-                         ;; We meet early to prune the csets to a reasonable size.
-                         ;; This weakens the inference a bit, but sometimes avoids
-                         ;; constraint explosion.
+            ;; We meet early to prune the csets to a reasonable size.
+            ;; This weakens the inference a bit, but sometimes avoids
+            ;; constraint explosion.
             (% cset-meet (cgen context s t obj) expected-cset)))))
 
 
@@ -1031,16 +1064,17 @@
 ;; like infer, but T-var is the vararg type:
 (define (infer/vararg X Y S T T-var R [expected #f]
                       #:objs [objs '()])
-  (and ((length S) . >= . (length T))
-       (let* ([fewer-ts (- (length S) (length T))]
-              [new-T (match T-var
-                       [(? Type? var-t) (list-extend S T var-t)]
-                       [(Rest: rst-ts)
-                        #:when (zero? (remainder fewer-ts (length rst-ts)))
-                        (append T (repeat-list rst-ts
-                                               (quotient fewer-ts (length rst-ts))))]
-                       [_ T])])
-         (infer X Y S new-T R expected #:objs objs))))
+  (parameterize ([infered-tvar-map (hash)])
+    (and ((length S) . >= . (length T))
+         (let* ([fewer-ts (- (length S) (length T))]
+                [new-T (match T-var
+                         [(? Type? var-t) (list-extend S T var-t)]
+                         [(Rest: rst-ts)
+                          #:when (zero? (remainder fewer-ts (length rst-ts)))
+                          (append T (repeat-list rst-ts
+                                                 (quotient fewer-ts (length rst-ts))))]
+                         [_ T])])
+           (infer X Y S new-T R expected #:objs objs)))))
 
 ;; like infer, but dotted-var is the bound on the ...
 ;; and T-dotted is the repeated type
diff --git a/typed-racket-lib/typed-racket/private/parse-type.rkt b/typed-racket-lib/typed-racket/private/parse-type.rkt
index 64a7412da..ec55ceffd 100644
--- a/typed-racket-lib/typed-racket/private/parse-type.rkt
+++ b/typed-racket-lib/typed-racket/private/parse-type.rkt
@@ -193,6 +193,11 @@
            (parse-literal-alls #'t.type))]
     [_ null]))
 
+(define-syntax-class maybe-bounded
+  #:datum-literals (<:)
+  #:attributes (name bound)
+  (pattern (name:id <: bound:expr))
+  (pattern name:id #:attr bound #f))
 
 ;; Syntax -> Type
 ;; Parse a Forall type
@@ -215,7 +220,21 @@
                     "variable" (syntax-e maybe-dup)))
      (let* ([vars (stx-map syntax-e #'(vars ...))])
        (extend-tvars vars
-         (make-Poly vars (parse-type #'t.type))))]
+                     (make-Poly vars (parse-type #'t.type))))]
+    [(:All^ (vars:maybe-bounded ...) . t:omit-parens)
+     (define maybe-dup (check-duplicate-identifier (attribute vars.name)))
+     (when maybe-dup
+       (parse-error "duplicate type variable"
+                    "variable" (syntax-e maybe-dup)))
+     (define bounds (for/fold ([acc (hash)])
+                              ([i (stx-map syntax-e (attribute vars.name))]
+                               [j (attribute vars.bound)]
+                               #:when j)
+                      (hash-set acc i
+                                (extend-tvars (hash-keys acc) (parse-type j)))))
+     (let* ([vars (stx-map syntax-e (attribute vars.name))])
+       (extend-tvars vars
+                     (make-Poly vars (parse-type #'t.type) #:bounds bounds)))]
     ;; Next two are row polymorphic cases
     [(:All^ (var:id #:row) . t:omit-parens)
      (add-disappeared-use #'kw)
diff --git a/typed-racket-lib/typed-racket/rep/type-rep.rkt b/typed-racket-lib/typed-racket/rep/type-rep.rkt
index 257eb1523..334aed47b 100644
--- a/typed-racket-lib/typed-racket/rep/type-rep.rkt
+++ b/typed-racket-lib/typed-racket/rep/type-rep.rkt
@@ -24,6 +24,7 @@
          syntax/id-set
          racket/contract
          racket/lazy-require
+         racket/syntax
          racket/unsafe/undefined
          (for-syntax racket/base
                      racket/syntax
@@ -46,6 +47,9 @@
          PolyDots-unsafe:
          Mu? Poly? PolyDots? PolyRow?
          Poly-n
+         F-n
+         F-bound
+         F?
          PolyDots-n
          Class? Row? Row:
          free-vars*
@@ -84,6 +88,8 @@
                      [PolyDots:* PolyDots:]
                      [PolyRow:* PolyRow:]
                      [Mu* make-Mu]
+                     [F* make-F]
+                     [F:* F:]
                      [make-Mu unsafe-make-Mu]
                      [Poly* make-Poly]
                      [PolyDots* make-PolyDots]
@@ -105,6 +111,7 @@
       (App? x)))
 
 (lazy-require
+ ("../types/substitute.rkt" (subst))
  ("../types/overlap.rkt" (overlap?))
  ("../types/prop-ops.rkt" (-and))
  ("../types/resolve.rkt" (resolve-app))
@@ -139,13 +146,26 @@
 
 ;; free type variables
 ;; n is a Name
-(def-type F ([n symbol?])
+(def-type F ([n symbol?]
+             [bound (or/c #f Type?)])
+  #:no-provide
   [#:frees
    [#:vars (_) (single-free-var n)]
    [#:idxs (_) empty-free-vars]]
   [#:fmap (_ #:self self) self]
   [#:for-each (_) (void)])
 
+(define (F* n [bound #f])
+  (make-F n bound))
+
+
+(define-match-expander F:*
+  (lambda (stx)
+    (syntax-case stx ()
+      [(_ n) #'(F: n _)]
+      [(_ n b) #'(F: n b)])))
+
+
 (define Name-table (make-free-id-table))
 
 ;; Name, an indirection of a type through the environment
@@ -519,10 +539,14 @@
 ;; n is how many variables are bound here
 ;; body is a type
 (def-type Poly ([n exact-nonnegative-integer?]
+                [bounds (hash/c exact-nonnegative-integer?
+                                Type?
+                                #:immutable #t
+                                #:flat #t)]
                 [body Type?])
   #:no-provide
   [#:frees (f) (f body)]
-  [#:fmap (f) (make-Poly n (f body))]
+  [#:fmap (f) (make-Poly n bounds (f body))]
   [#:for-each (f) (f body)]
   [#:mask (λ (t) (mask (Poly-body t)))])
 
@@ -1456,7 +1480,7 @@
       ;; De Bruijn indices
       [(B: idx) (transform idx lvl cur #f)]
       ;; Type variables
-      [(F: var) (transform var lvl cur #f)]
+      [(F: var _) (transform var lvl cur #f)]
       ;; forms w/ dotted type vars/indices
       [(RestDots: ty d)
        (make-RestDots (rec ty) (transform d lvl d #t))]
@@ -1477,8 +1501,8 @@
        (make-PolyRow constraints (rec/lvl body (add1 lvl)))]
       [(PolyDots: n body)
        (make-PolyDots n (rec/lvl body (+ n lvl)))]
-      [(Poly: n body)
-       (make-Poly n (rec/lvl body (+ n lvl)))]
+      [(Poly: n bounds body)
+       (make-Poly n bounds (rec/lvl body (+ n lvl)))]
       [_ (Rep-fmap cur rec)])))
 
 
@@ -1618,7 +1642,7 @@
 (define (Mu-body* name t)
   (match t
     [(Mu: body)
-     (instantiate-type body (make-F name))]))
+     (instantiate-type body (F* name))]))
 
 ;; unfold : Mu -> Type
 (define/cond-contract (unfold t)
@@ -1638,19 +1662,42 @@
 ;;
 ;; list<symbol> type #:original-names list<symbol> -> type
 ;;
-(define (Poly* names body #:original-names [orig names])
+
+(define (Poly* names body #:bounds [bounds '#hash()] #:original-names [orig names])
   (if (null? names) body
-      (let ([v (make-Poly (length names) (abstract-type body names))])
+      (let* ([len (length names)]
+             [new-bounds (for/hash ([(n v) bounds])
+                           (values (index-of names n) v))]
+             [v (make-Poly len new-bounds (abstract-type body names))])
         (hash-set! type-var-name-table v orig)
         v)))
 
+(define (unsubst ty orig-names names)
+  (for/fold ([acc ty])
+            ([o orig-names]
+             [n names])
+    (subst o (make-F n #f) acc)
+    #;
+    (subst o (make-Name (format-id #f "~a" n) 0 #f) acc)))
+
 ;; Poly 'smart' destructor
 (define (Poly-body* names t)
+  (define orig-names (hash-ref type-var-name-table t null))
   (match t
-    [(Poly: n body)
+    [(Poly: n bounds body)
+     (define new-bounds (for/hash ([(idx v) bounds])
+                          (values (list-ref names idx) (unsubst v orig-names names))))
      (unless (= (length names) n)
        (int-err "Wrong number of names: expected ~a got ~a" n (length names)))
-     (instantiate-type body (map make-F names))]))
+     (instantiate-type body
+                       (map (lambda (n)
+                              (define v (match (hash-ref new-bounds n #f)
+                                          [(App: rator (list (F: vb _)))
+                                           #:when (hash-has-key? new-bounds vb)
+                                           (make-App rator (list (hash-ref new-bounds vb)))]
+                                          [_else _else]))
+                              (make-F n v))
+                        names))]))
 
 ;; PolyDots 'smart' constructor
 (define (PolyDots* names body)
@@ -1665,7 +1712,7 @@
     [(PolyDots: n body)
      (unless (= (length names) n)
        (int-err "Wrong number of names: expected ~a got ~a" n (length names)))
-     (instantiate-type body (map make-F names))]))
+     (instantiate-type body (map F* names))]))
 
 
 ;; PolyRow 'smart' constructor
@@ -1683,7 +1730,7 @@
 (define (PolyRow-body* names t)
   (match t
     [(PolyRow: constraints body)
-     (instantiate-type body (map make-F names))]))
+     (instantiate-type body (map F* names))]))
 
 
 ;;***************************************************************
@@ -1939,7 +1986,7 @@
     [(Some: n body)
      (unless (= (length names) n)
        (int-err "Wrong number of names: expected ~a got ~a" n (length names)))
-     (instantiate-type body (map make-F names))]))
+     (instantiate-type body (map F* names))]))
 
 
 (define-match-expander Some-names:
diff --git a/typed-racket-lib/typed-racket/types/printer.rkt b/typed-racket-lib/typed-racket/types/printer.rkt
index 7abb422d8..8a75d1dd5 100644
--- a/typed-racket-lib/typed-racket/types/printer.rkt
+++ b/typed-racket-lib/typed-racket/types/printer.rkt
@@ -714,10 +714,11 @@
     [(? Base?) (Base-name type)]
     [(Pair: l r) `(Pairof ,(t->s l) ,(t->s r))]
     [(ListDots: dty dbound) `(List ,(t->s dty) ... ,dbound)]
-    [(F: nm)
+    [(F: nm bound)
      (cond
        [(eq? nm imp-var) "Imp"]
        [(eq? nm self-var) "Self"]
+       [(Type? bound) (format "~a <: ~a" nm (t->s bound))]
        [else nm])]
     [(Param: in out)
      (if (equal? in out)
diff --git a/typed-racket-lib/typed-racket/types/subtype.rkt b/typed-racket-lib/typed-racket/types/subtype.rkt
index 3d580858e..3673eb946 100644
--- a/typed-racket-lib/typed-racket/types/subtype.rkt
+++ b/typed-racket-lib/typed-racket/types/subtype.rkt
@@ -802,11 +802,12 @@
    (match t2
      [(Evt: result2) (subtype* A result1 result2)]
      [_ (continue<: A t1 t2 obj)])]
-  [(case: F (F: var1))
-   (match t2
+  [(case: F (F: var1 bound))
+   (match* (t2 bound)
      ;; tvars are equal if they are the same variable
-     [(F: var2) (and (eq? var1 var2) A)]
-     [_ (continue<: A t1 t2 obj)])]
+     [((F: var2) _) (and (eq? var1 var2) A)]
+     [(_ (? Type?)) (subtype* A bound t2 obj)]
+     [(_ _) (continue<: A t1 t2 obj)])]
   [(case: Fun (Fun: arrows1))
    (match* (t2 arrows1)
      ;; special case when t1 can be collapsed into simpler arrow
diff --git a/typed-racket-test/fail/bounded-poly.rkt b/typed-racket-test/fail/bounded-poly.rkt
new file mode 100644
index 000000000..9f23e6b81
--- /dev/null
+++ b/typed-racket-test/fail/bounded-poly.rkt
@@ -0,0 +1,9 @@
+#lang typed/racket/base
+
+(: a-func (All ([X <: Integer])
+               (-> X String)))
+(define (a-func a)
+  (number->string a))
+
+
+(a-func 19.999) ;; fail
diff --git a/typed-racket-test/main.rkt b/typed-racket-test/main.rkt
index d40e4a308..a131c5639 100644
--- a/typed-racket-test/main.rkt
+++ b/typed-racket-test/main.rkt
@@ -192,7 +192,7 @@
   (define missed-opt? (make-parameter #f))
   (define bench? (make-parameter #f))
   (define math? (make-parameter #f))
-  (define excl (make-parameter (list)))
+  (define excl (make-parameter (set)))
   (define single (make-parameter #f))
   (current-namespace (make-base-namespace))
   (command-line
diff --git a/typed-racket-test/succeed/bounded-poly.rkt b/typed-racket-test/succeed/bounded-poly.rkt
new file mode 100644
index 000000000..445db0bd9
--- /dev/null
+++ b/typed-racket-test/succeed/bounded-poly.rkt
@@ -0,0 +1,26 @@
+#lang typed/racket/base
+
+(: a-func (All ([X <: Integer])
+               (-> X String)))
+(define (a-func a)
+  (number->string a))
+
+
+(a-func 10) ;; pass
+
+
+(struct (A) foo ([a : A]) #:type-name Foo)
+
+(: c-func (All ([X <: Integer] [Y <: (Foo X)])
+               (-> X Y String)))
+(define (c-func a b)
+  (number->string a))
+
+(c-func 10 (foo 10))
+
+(: d-func (All ([X <: Integer] [Y <: (Foo X)])
+               (-> X Y String)))
+(define (d-func a b)
+  (number->string (foo-a b)))
+
+(d-func 42 (foo 10))