We conduct a code search restricted to the recently introduced class of generalized punctured convolutional codes (GPCCs) to find good unequal error protection (UEP) convolutional codes for a prescribed minimal trellis complexity. The trellis complexity is taken to be the number of symbols per information bit in the “minimal” trellis module for the code. The GPCC class has been shown to possess codes with good distance properties under this decoding complexity measure. New good UEP convolutional codes and their respective effective free distances are tabulated for a variety of code rates and “minimal” trellis complexities. These codes can be used in several applications that require different levels of protection for their bits, such as the hierarchical digital transmission of video or images.