Models for pricing interest rate claims, developed under the Heath-Jarrow-Morton paradigm, differ according to the volatility structure imposed on forward rates. For most general HJM structures the resultant path dependence creates implementation problems. Ritchken and Sankarasubramanian have recently identified necessary and sufficient conditions on the class of volatility structures of forward rates that enable the term structure dynamics to be captured by a finite set of state variables. The class is quite rich. The instantaneous spot rate volatility may be quite general, but the model curtails the structure of forward rate volatilities relative to this spot rate volatility. This paper provides empirical tests for this class of volatility structures. Unlike other studies, the volatility structure is examined over the a broad section of maturities in the yield curve. Using Treasury data over the period 1982-1994, we find support for this class. Furthermore, unlike other studies, no evidence of a "volatility" hump is identified.