Recent studies of counterion-induced condensation of nucleic acid helices into aggregates produced several puzzling observations. For instance, trivalent cobalt hexamine ions condensed double-stranded (ds) DNA oligomers but not their more highly charged dsRNA counterparts. Divalent alkaline earth metal ions condensed triple-stranded (ts) DNA oligomers but not dsDNA. Here we show that these counterintuitive experimental results can be rationalized within the electrostatic zipper model of interactions between molecules with helical charge motifs. We report statistical mechanical calculations that reveal dramatic and nontrivial interplay between the effects of helical structure and thermal fluctuations on electrostatic interaction between oligomeric nucleic acids. Combining predictions for oligomeric and much longer helices, we also interpret recent experimental studies of the role of counterion charge, structure, and chemistry. We argue that an electrostatic zipper attraction might be a major or even dominant force in nucleic acid condensation.