  Ornstein and Shields (Advances in Math., 10:143-146, 1973) proved that
Brownian motion reflected on a bounded region is an infinite entropy Bernoulli
flow and thus Ornstein theory yielded the existence of a measure-preserving
isomorphism between any two such Brownian motions. For fixed h >0, we construct
by elementary methods, isomorphisms with almost surely finite coding windows
between Brownian motions reflected on the intervals [0, qh] for all positive
rationals q.
