  We have used the VLA to image the HI 21-cm line emission in the edge-on Sd
galaxy IC2233 and the blue compact dwarf NGC2537. We also present new optical
B,R, and H alpha imaging of IC2233 obtained with the WIYN telescope. Despite
evidence of localized massive star formation, IC2233 has a low surface
brightness disk with a low global star formation rate (~0.05 M_sun/yr), and no
significant 21-cm radio continuum emission. The HI and ionized gas disks of
IC2233 are clumpy and vertically distended, with scale heights comparable to
the young stars. Both the stellar and HI disks of IC2233 appear flared, and we
also find a vertically extended, rotationally anomalous HI component extending
to z~2.4 kpc. The HI disk exhibits a mild lopsidedness as well as a global
corrugation pattern with a period of ~7 kpc and an amplitude of ~150 pc. To our
knowledge, this is the first time corrugations of the gas disk have been
reported in an external galaxy; these undulations may be linked to bending
instabilities or to underlying spiral structure and suggest that the disk is
largely self-gravitating.
  Lying at a projected distance of 16.7' from IC2233, NGC2537 has an HI disk
with a bright, tilted inner ring and a flocculent, dynamically cold outer
region that extends to ~3.5D_25. Although NGC2537 is rotationally-dominated, it
shows significant turbulence near its center. The inner rotation curve rises
steeply, implying a strong central mass concentration. Our data indicate that
IC2233 and NGC2537 do not constitute a bound pair and most likely lie at
different distances. We also find no compelling evidence of a recent minor
merger in either galaxy, suggesting that both are examples of small disk
galaxies evolving in relative isolation. (Abridged)
