We propose five classes of variable length codes for encoding positive integers: One is a class of codes having constant Hamming weight. The other four classes of codes have a prefix and a suffix in a codeword. The prefix indicates the weight or the length of the suffix and variable length constant weight codes are used for the prefixes and the suffixes of some of these codes. For encoding of these codes we can use Schalkwijk's algorithm. It is shown that some of the proposed codes are universal and asymptotically optimal in the meaning that P. Elias has defined. We compare them with other known codes from the viewpoints of the length of the codewords corresponding to integers 2M (M=0, 1, , 30) and the average codeword length for two sources: 26 letters in English sentences and the geometrically distributed positive integers. The results shows that some of the proposed codes which are universal and asymptotically optimal are more efficient than the known codes.