We show a simple method to control both the stability and the self-assembly behavior of DNA structures. By connecting two adjacent duplexes with small synthetic linkers, factors such as linker rigidity and DNA strand orientation can increase the thermal denaturation temperature of 17 base-pair duplexes by up to 10 degrees C, and significantly increase the cooperativity of melting of the two duplexes. The same DNA sequence can thus be tuned to melt at vastly different temperatures by selecting the linker structure and DNA-to-linker connectivity. In addition, a small rigid m-triphenylene linker directly affects the self-assembly product distribution. With this linker, changes in the orientation of the linked strands (e.g., 5'3' vs 3'3') can lead to dramatic changes in the self-assembly behavior, from the formation of cyclic dimer and tetramer to higher-order oligomers. These variations can be readily predicted using a simple strand-end alignment model.