diff --git a/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-1.rkt b/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-1.rkt
index bc56894d39..ab5c7f85eb 100644
--- a/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-1.rkt
+++ b/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-1.rkt
@@ -290,4 +290,4 @@
       (ins-preserves-rb-tree t)))
 
 (define (generate-enum-term)
-  (generate-term rbtrees t #:i-th (pick-an-index)))
+  (generate-term rbtrees t #:i-th (pick-an-index 0.2)))
diff --git a/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-2.rkt b/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-2.rkt
index 9efe31f832..40f25671c5 100644
--- a/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-2.rkt
+++ b/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-2.rkt
@@ -288,4 +288,4 @@
       (ins-preserves-rb-tree t)))
 
 (define (generate-enum-term)
-  (generate-term rbtrees t #:i-th (pick-an-index)))
+  (generate-term rbtrees t #:i-th (pick-an-index 0.2)))
diff --git a/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-3.rkt b/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-3.rkt
index ae26468d7e..3c319bbe53 100644
--- a/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-3.rkt
+++ b/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-3.rkt
@@ -290,4 +290,4 @@
       (ins-preserves-rb-tree t)))
 
 (define (generate-enum-term)
-  (generate-term rbtrees t #:i-th (pick-an-index)))
+  (generate-term rbtrees t #:i-th (pick-an-index 0.2)))
diff --git a/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-base.rkt b/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-base.rkt
index 9cbbce763a..aaa4491840 100644
--- a/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-base.rkt
+++ b/pkgs/redex-pkgs/redex-examples/redex/examples/benchmark/rbtrees/rbtrees-base.rkt
@@ -290,4 +290,4 @@
       (ins-preserves-rb-tree t)))
 
 (define (generate-enum-term)
-  (generate-term rbtrees t #:i-th (pick-an-index)))
+  (generate-term rbtrees t #:i-th (pick-an-index 0.2)))
diff --git a/pkgs/redex-pkgs/redex-lib/redex/private/generate-term.rkt b/pkgs/redex-pkgs/redex-lib/redex/private/generate-term.rkt
index 3787ef9fb0..4e10b6e22d 100644
--- a/pkgs/redex-pkgs/redex-lib/redex/private/generate-term.rkt
+++ b/pkgs/redex-pkgs/redex-lib/redex/private/generate-term.rkt
@@ -287,10 +287,10 @@
        (values (enum-ith enum (random-natural the-size))
                'ignored))]))
 
-(define (pick-an-index)
-  (max (random-natural/no-mean 0.01)
-       (random-natural/no-mean 0.01)
-       (random-natural/no-mean 0.01)))
+(define (pick-an-index [prob-of-zero 0.01])
+  (max (random-natural/no-mean prob-of-zero)
+       (random-natural/no-mean prob-of-zero)
+       (random-natural/no-mean prob-of-zero)))
 
 ;; (: random-natural/no-mean (-> Real Natural))
 (define (random-natural/no-mean prob-zero)