Embedded processors often accommodate two instruction sets, a standard instruction set and a compressed instruction set. With the compressed instruction set, code size can be reduced while instruction count (and consequently execution time) can be increased. To achieve code size reduction without significant increase of execution time, this paper proposes a new compressed instruction set architecture, called TOE (Two Operations Execution). The proposed instruction set format includes the parallel bit that indicates an instruction can be executed simultaneously with the next instruction. To add the parallel bit, TOE instruction format reduces the destination register field. The reduction of the register field limits the number of registers that are accessible by an instruction. To overcome the limited accessibility of registers, TOE adapts non-homogeneous register partition in which registers are divided into multiple subsets, each of which are accessed by different groups of instructions. With non-homogeneous registers, each instruction can access only a limited number of registers, but an entire program can access all available registers. With efficient non-homogeneous register allocator, all registers can be used in a balanced manner. As a result, the increase of code size due to register spills is negligible. Experimental results show that more than 30% of TOE instructions can be executed in parallel without significant increase of code size when compared to existing Thumb instruction set.