This paper describes the retargeting and further enhancement of a compact multitasking kernel for the 32-bit Altera Nios II processor. The kernel, called QUERK for Queen's University Educational Real-time Kernel, was originally written in assembly language and then the C language for the Motorola (and then Freescale) 68HC11 processor. Consisting of less than 200 lines of assembly-language instructions, the kernel was intended for educational purposes on undergraduate laboratory equipment in use at the time it was created. The software also supported undergraduate capstone project activity. To migrate the software to the 32-bit Altera Nios II processor that subsequently replaced the 8-bit 68HC11 in undergraduate laboratory activity, and to investigate issues arising from differences between the two instruction sets, this paper describes the retargeting of the kernel at the level of assembly language. The results reveal that the number of assembly-language source instructions for the base kernel with relinquish, block, and unblock services increased by less than 9% for the Nios II in comparison to the 68HC11. Although many additional instructions are needed to save and restore the larger number of registers for the Nios II, reductions in the number of instructions needed in other parts of the kernel aid in offsetting that increase in instructions. Further enhancements of the kernel are also described with support for timer delay requests, dynamic memory management, and interprocess communication with message passing. Potential future enhancements are also described.