diff --git a/collects/typed-scheme/private/base-types.rkt b/collects/typed-scheme/private/base-types.rkt
index 44d75e8e..9f05fa4d 100644
--- a/collects/typed-scheme/private/base-types.rkt
+++ b/collects/typed-scheme/private/base-types.rkt
@@ -16,17 +16,34 @@
 [Nonpositive-Inexact-Real -NonPosInexactReal]
 [Nonpositive-Single-Flonum -NonPosSingleFlonum]
 [Negative-Inexact-Real -NegInexactReal]
+[Negative-Single-Flonum -NegSingleFlonum]
 [Nonnegative-Inexact-Real -NonNegInexactReal]
 [Nonnegative-Single-Flonum -NonNegSingleFlonum]
 [Positive-Inexact-Real -PosInexactReal]
+[Positive-Single-Flonum -PosSingleFlonum]
 [Inexact-Real-Zero -InexactRealZero]
 [Inexact-Real-Negative-Zero -InexactRealNegZero]
 [Inexact-Real-Positive-Zero -InexactRealPosZero]
 [Single-Flonum-Zero -SingleFlonumZero]
-[Float -Flonum] ; these are the default, 64-bit floats, can be optimized
-[Nonpositive-Float -NonPosFlonum]
-[Nonnegative-Float -NonNegFlonum]
-[Float-Zero -FlonumZero]
+[Single-Flonum-Negative-Zero -SingleFlonumNegZero]
+[Single-Flonum-Positive-Zero -SingleFlonumPosZero]
+;; these are the default, 64-bit floats, can be optimized
+[Float -Flonum] ; both of these are valid
+[Flonum -Flonum]
+[Nonpositive-Float -NonPosFlonum] ; both of these are valid
+[Nonpositive-Flonum -NonPosFlonum]
+[Negative-Float -NegFlonum] ; both of these are valid
+[Negative-Flonum -NegFlonum]
+[Nonnegative-Float -NonNegFlonum] ; both of these are valid
+[Nonnegative-Flonum -NonNegFlonum]
+[Positive-Float -PosFlonum] ; both of these are valid
+[Positive-Flonum -PosFlonum]
+[Float-Zero -FlonumZero] ; both of these are valid
+[Flonum-Zero -FlonumZero]
+[Float-Negative-Zero -FlonumNegZero] ; both of these are valid
+[Flonum-Negative-Zero -FlonumNegZero]
+[Float-Positive-Zero -FlonumPosZero] ; both of these are valid
+[Flonum-Positive-Zero -FlonumPosZero]
 [Exact-Rational -Rat]
 [Nonpositive-Exact-Rational -NonPosRat]
 [Negative-Exact-Rational -NegRat]
diff --git a/collects/typed-scheme/types/numeric-tower.rkt b/collects/typed-scheme/types/numeric-tower.rkt
index f041e3c9..a27d4b8e 100644
--- a/collects/typed-scheme/types/numeric-tower.rkt
+++ b/collects/typed-scheme/types/numeric-tower.rkt
@@ -7,13 +7,34 @@
          unstable/function
          (for-template racket/base racket/contract racket/flonum (types numeric-predicates)))
 
-(provide (all-defined-out))
+(provide portable-fixnum? portable-index?
+         -Zero -One -PosByte -Byte -PosIndex -Index
+         -PosFixnum -NonNegFixnum -NegFixnum -NonPosFixnum -Fixnum
+         -PosInt -Nat -NegInt -NonPosInt -Int
+         -PosRat -NonNegRat -NegRat -NonPosRat -Rat
+         -FlonumPosZero -FlonumNegZero -FlonumZero -PosFlonum -NonNegFlonum -NegFlonum -NonPosFlonum -Flonum
+         -SingleFlonumPosZero -SingleFlonumNegZero -SingleFlonumZero -PosSingleFlonum -NonNegSingleFlonum -NegSingleFlonum -NonPosSingleFlonum -SingleFlonum
+         -InexactRealPosZero -InexactRealNegZero -InexactRealZero -PosInexactReal -NonNegInexactReal -NegInexactReal -NonPosInexactReal -InexactReal
+         -RealZero -PosReal -NonNegReal -NegReal -NonPosReal -Real
+         -FloatComplex -SingleFlonumComplex -InexactComplex -Number
+         ;; for backward compatibility
+         (rename-out [-NonNegFlonum -NonnegativeFlonum]
+                     [-Rat -ExactRational]
+                     [-Int -Integer]
+                     [-PosInt -ExactPositiveInteger]
+                     [-PosFixnum -PositiveFixnum]
+                     [-NegFixnum -NegativeFixnum]
+                     [-NonNegFixnum -NonnegativeFixnum]
+                     [-Nat -ExactNonnegativeInteger]))
+
 
 ;; Numeric hierarchy
 ;; All built as unions of non-overlapping base types.
 ;; This should make encoding mathematical properties in the base env easier.
-;; Most of the weird base types will probably never be exposed to the user
-;; and some probably won't show up in the base env either.
+;; The base types that don't have an interesting mathematical meaning
+;; (e.g. -Byte>1, -PosFixnumNotIndex, etc.) should not be used anywhere, as
+;; they should not be exposed to the user and could easily be misused in
+;; the base type environment. They are not provided.
 ;; A lot of these contracts will be overriden in type->contract, so their
 ;; hairiness should not be of much consequence.
 
@@ -223,13 +244,3 @@
              #'-ExactComplexNotReal))
 (define -Complex (*Un -Real -InexactComplex -ExactComplexNotReal))
 (define -Number -Complex)
-
-;; TODO for compatibility
-(define -NonnegativeFlonum -NonNegFlonum)
-(define -ExactRational -Rat)
-(define -Integer -Int)
-(define -ExactPositiveInteger -PosInt)
-(define -PositiveFixnum -PosFixnum)
-(define -NegativeFixnum -NegFixnum)
-(define -NonnegativeFixnum -NonNegFixnum)
-(define -ExactNonnegativeInteger -Nat)