For some applications where the speed of decoding and the fault tolerance are important, like in video storing, one of the successful answers is Fix-Free Codes. These codes have been applied in some standards like H.263+ and MPEG-4. The cost of using fix-free codes is to increase the redundancy of the code which means the increase in the amount of bits we need to represent any peace of information. Thus we investigated the use of Huffman Codes with low and negligible backward decoding delay. We showed that for almost all cases there is always a Minimum Delay Huffman Code for a given length vector. The average delay of this code for anti-uniform sources is calculated, that is in agreement with the simulations, and it is shown that this delay is one bit for large alphabet sources. Also an algorithm is proposed which will find the minimum delay code with a good performance.