diff --git a/TUTORIAL.org b/TUTORIAL.org
index 823b1a7..af1568b 100644
--- a/TUTORIAL.org
+++ b/TUTORIAL.org
@@ -169,7 +169,7 @@ out the elements in the same order, every time.
 When combined with binary serialization, this is Preserves' "canonical
 form".
 This is important and useful for many contexts, but especially for
-cryptographic signatures.
+cryptographic signatures and hashing.
 
 #+BEGIN_SRC preserves
 @"This hand-typed Preserves document..."
@@ -185,8 +185,10 @@ cryptographic signatures.
           "noise": "ooh-ooh"}}
 #+END_SRC
 
-This is a bit more expensive than normal serialization (because
-sorting needs to occur), but is still quite fast in general.
+Clever implementations can get canonicalized output for free by
+carefully ordering set elements and dictionary entries at construction
+time, but even in simple implementations, canonical serialization is
+almost as cheap as normal serialization.
 
 ** Defining our own types using Records