This brief proposes a modified version of the popular lifting algorithm of Daubechies-4 (D4) and Daubechies-6 (D6) wavelets and its efficient implementation using integer polynomial mapping (IPM). At first, an improved polyphase matrix for D4 is presented that eliminates one filter coefficient completely without losing any accuracy. Then, IPM is applied to encode the remaining irrational coefficients. As a result, computation error due to irrational numbers in the conventional method is significantly reduced, resulting in better image reconstruction. For D6, a two-level optimization scheme combined with the resource sharing of coefficients is applied that results in simplified hardware architecture with much fewer resources.