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We have used the VLA to image the HI 21-cm line emission in the edge-on Sdgalaxy IC2233 and the blue compact dwarf NGC2537. We also present new opticalB,R, and H alpha imaging of IC2233 obtained with the WIYN telescope. Despiteevidence of localized massive star formation, IC2233 has a low surfacebrightness disk with a low global star formation rate (~0.05 M_sun/yr), and nosignificant 21-cm radio continuum emission. The HI and ionized gas disks ofIC2233 are clumpy and vertically distended, with scale heights comparable tothe young stars. Both the stellar and HI disks of IC2233 appear flared, and wealso find a vertically extended, rotationally anomalous HI component extendingto z~2.4 kpc. The HI disk exhibits a mild lopsidedness as well as a globalcorrugation pattern with a period of ~7 kpc and an amplitude of ~150 pc. To ourknowledge, this is the first time corrugations of the gas disk have beenreported in an external galaxy; these undulations may be linked to bendinginstabilities or to underlying spiral structure and suggest that the disk islargely self-gravitating.  Lying at a projected distance of 16.7' from IC2233, NGC2537 has an HI diskwith a bright, tilted inner ring and a flocculent, dynamically cold outerregion that extends to ~3.5D_25. Although NGC2537 is rotationally-dominated, itshows significant turbulence near its center. The inner rotation curve risessteeply, implying a strong central mass concentration. Our data indicate thatIC2233 and NGC2537 do not constitute a bound pair and most likely lie atdifferent distances. We also find no compelling evidence of a recent minormerger in either galaxy, suggesting that both are examples of small diskgalaxies evolving in relative isolation. (Abridged)

HI Imaging Observations of Superthin Galaxies. II. IC2233 and the Blue Compact Dwarf NGC2537