Optimal asset replacement is analysed under non-exponential technological improvement, whereby the asset capital cost and the operational cost reduce for newer assets, and the relative rate of this decrease varies with time. We establish that the optimal lifetime of sequentially replaced assets increases if the relative rate of technological change decreases, and converse. Next, the two-cycle replacement algorithm is employed to take the unequal asset lifetime into account. The algorithm is adjusted to the case of several discrete estimates of changing asset costs and demonstrates good performance in various scenarios of improving technology.