Fiber which dispersion decreases with distance in exponential power can overcome the effect induced by loss on soliton propagation. We can obtain this character by using core-radius decreasing fiber, exponentially continual decreasing or discrete decreasing (ladder fiber). Continual variation of radius will produce modes coupling. After analyses, in the continual core-radius decreasing fiber, even if v equals 2.4048, there will still be two modesc. One is stable mode when z yields (infinity) , the other is a special mode with both characters of transmission mode and of radiation mode which we called transition mode. It has the same transmission constant as the exciting mode, but its amplitude reduces at the decreasing ratio of core-radius. The effect of transition mode always exists in the exponential decreasing fiber, in spite that it can efficiently increase the distance of soliton propagation. There is no transition mode in the ladder fiber, but each section of this fiber will be shorter. In order to evaluate the transmission distance of the stable mode ground state soliton, we calculate it with the ratio of local power and threshold power, and call it threshold degree. If the ground-state soliton has the power of threshold before entering the core-radius decreasing fiber, the threshold degree of stable soliton is equal to the ratio of the order parameter of soliton N2. Difference of the threshold degree between ladder fiber and exponential fiber is so little that there is almost no distinctness between them. The formula and curves of the threshold degree are given at the end of this article, which mean the preceding transmission distance in fibers.