diff --git a/cover.rkt b/cover.rkt
index 44f7bcf..60bd56e 100644
--- a/cover.rkt
+++ b/cover.rkt
@@ -191,13 +191,8 @@ in "coverage.rkt". This raw coverage information is converted to a usable form b
 (define (clear-coverage!)
   (current-cover-environment (make-cover-environment)))
 
-(define (make-kernel-namespace)
-  (define ns (make-empty-namespace))
-  (define cns (current-namespace))
-  (namespace-attach-module cns ''#%builtin ns)
-  ns)
-
-(define (make-cover-environment [ns (make-kernel-namespace)])
+(define (make-cover-environment [ns (make-empty-namespace)])
+  (kernelize-namespace! ns)
   (parameterize ([current-namespace ns])
     (define ann (load-annotate-top))
     (environment
@@ -206,6 +201,10 @@ in "coverage.rkt". This raw coverage information is converted to a usable form b
      ann
      (load-raw-coverage))))
 
+(define (kernelize-namespace! ns)
+  (define cns (current-namespace))
+  (namespace-attach-module cns ''#%builtin ns))
+
 (define (get-annotate-top)
   (get-val environment-ann-top))
 (define (load-annotate-top)
diff --git a/scribblings/api.scrbl b/scribblings/api.scrbl
index aa29000..3656eb1 100644
--- a/scribblings/api.scrbl
+++ b/scribblings/api.scrbl
@@ -88,7 +88,7 @@ Tests if the given value is a coverage environment.}
 @defparam[current-cover-environment environment environment?
           #:value (make-cover-environment)]{
 The current coverage environment. Defaults to an environment built from
-@racket[make-empty-namespace]}
+@racket[make-empty-namespace].}
 @defproc[(environment-namespace [environment environment?]) namespace?]{
 Get the namespace that coverage should be run in. This is the same namespace given to
 @racket[make-cover-environment]}
@@ -101,4 +101,6 @@ annotations.  That code must be run in @racket[environment]'s namespace.}
 @defproc[(make-cover-environment [namespace namespace? (make-empty-namespace)]) environment?]{
 
 Makes a coverage environment such that @racket[environment-namespace] will return
-@racket[namespace], and @racket[namespace] will be set up to handle coverage information.}
+@racket[namespace], and @racket[namespace] will be set up to handle coverage information. If
+@racket[namespace] has been used in a different environment the two environments will share coverage
+information.}