Central banks of many countries offer zero coupon bonds and encourage trading of these in secondary markets. Price data suggests that the uncertain behavior of forward interest rates, based on bond prices, can be simply described in terms of a principal component analysis. However, attempts to model this description have been frustrated by a mathematical difficulty--the most direct approach leads to models with exploding interest rates. That is, some probability of infinite rates, and the collapse of bond prices, appears in the mathematics. We first revisit this difficulty by describing the original HJM model of A. Morton. We then propose a correction to his model which allows crucial forward rates to remain finite over an extended time. We will discuss implications of this correction, and we also illustrate that the interest rate dynamics have a fairly explicit solution. As a result, pricing interest rate derivatives with this model appears to be convenient and straightforward.