This paper presents some multi-criterion concurrently-optimal （2

1

31） and （3

1

31） nonsystematic convolutional codes for sequential decoding. These codes are constructed with a computer using an algorithm of constructing nonsystematic convolutional codes found by Zhang Zhao-zhi. Some of convolutional code generators are given. The minimum distance dc（m） and column distance profile dc（0

h） of these codes are found to be optimal. The free distance d

of the （2

1） code is made up to 29-30

and of the （3

1） code up to 47-49. All of the multi-criterion concurrently-optimal nonsystematic convolutional codespresented in this paper are intransparent with the greatest column inverse-distance dc（m） so that we. will be able to reduce the computational

requirements for recognizing the 180° phase-ambiguity in sequential decoding. The （3

1

31） nonsystematic code presented in this paper has concurrently-optimal performance for both 1/2 and 1/3 coding rates.