diff --git a/lens/private/compound/join-hash.scrbl b/lens/private/compound/join-hash.scrbl
index f11dcf7..5fe63ab 100644
--- a/lens/private/compound/join-hash.scrbl
+++ b/lens/private/compound/join-hash.scrbl
@@ -3,7 +3,8 @@
 @(require "../doc-util/main.rkt")
 
 
-@defproc[(lens-join/hash [key any/c] [lens lens?] ... ...) lens?]{
+@defproc[(lens-join/hash [key key/c] [lens (lens/c target/c value/c)] ... ...)
+         (lens/c target/c (hash/c key/c value/c #:immutable #t))]{
   Constructs a lens that combines the view of each
   @racket[lens] into a hash of views with @racket[key]s
   as the hash keys. In the same manner as @racket[lens-join/list],
diff --git a/lens/private/compound/join-list.scrbl b/lens/private/compound/join-list.scrbl
index e9f9cd1..e835b1c 100644
--- a/lens/private/compound/join-list.scrbl
+++ b/lens/private/compound/join-list.scrbl
@@ -2,7 +2,7 @@
 
 @(require "../doc-util/main.rkt")
 
-@defproc[(lens-join/list [lens lens?] ...) lens?]{
+@defproc[(lens-join/list [lens (lens/c target/c item/c)] ...) (lens/c target/c (listof item/c))]{
   Constructs a lens that combines the view of each
   @racket[lens] into a list of views. This lens can
   be used to view and set a list of values in a single
diff --git a/lens/private/compound/join-string.scrbl b/lens/private/compound/join-string.scrbl
index 8db5482..7d958fe 100644
--- a/lens/private/compound/join-string.scrbl
+++ b/lens/private/compound/join-string.scrbl
@@ -3,7 +3,7 @@
 @(require "../doc-util/main.rkt")
 
 
-@defproc[(lens-join/string [lens lens?] ...) lens?]{
+@defproc[(lens-join/string [lens (lens/c target/c char?)] ...) (lens/c target/c immutable-string?)]{
   Like @racket[lens-join/list], except the view is a string, not a list.
   Each @racket[lens] argument must return a @racket[char?] as a view.
   @lens-examples[
diff --git a/lens/private/compound/join-vector.scrbl b/lens/private/compound/join-vector.scrbl
index d8ea98f..66bda68 100644
--- a/lens/private/compound/join-vector.scrbl
+++ b/lens/private/compound/join-vector.scrbl
@@ -3,7 +3,8 @@
 @(require "../doc-util/main.rkt")
 
 
-@defproc[(lens-join/vector [lens lens?] ...) lens?]{
+@defproc[(lens-join/vector [lens (lens/c target/c item/c)] ...)
+         (lens/c target/c (vector-immutableof item/c))]{
   Like @racket[lens-join/list], except the view is a vector, not a list.
   @lens-examples[
     (define vector-first-third-fifth-lens