With its bulky volume, the ultraspectral sounder data might still suffer a few bits of error after channel coding. Therefore it is beneficial to incorporate some mechanism in source coding for error containment. The Tunstall code is a variableto-fixed length code which can reduce the error propagation encountered in fixed-to-variable length codes like Huffman and arithmetic codes. The original Tunstall code uses an exhaustive parse tree where internal nodes extend every symbol in branching. It might result in assignment of precious codewords to less probable parse strings. Based on an infinitely extended parse tree, a modified Tunstall code is proposed which grows an optimal non-exhaustive parse tree by assigning the complete codewords only to top probability nodes in the infinite tree. Comparison will be made among the original exhaustive Tunstall code, our modified non-exhaustive Tunstall code, the CCSDS Rice code, and JPEG-2000 in terms of compression ratio and percent error rate using the ultraspectral sounder data.