We have used the Very Large Array to image the H i 21-cm line emission in the edge-on Sd galaxy IC 2233 and the blue compact dwarf NGC 2537 . We also present new optical B , R , and H \alpha imaging of IC 2233 obtained with the WIYN telescope . Despite evidence of localized massive star formation in the form of prominent H ii regions and shells , supergiant stars , and a blue integrated color , IC 2233 has a low surface brightness disk with a very low global star formation rate ( ~ { } \hbox to 0.0 pt { $ < $ } { \lower 4.3 pt \hbox { $ \sim$ } } 0.05 M _ { \odot } yr ^ { -1 } ) , and no significant 21-cm radio continuum emission . The H i and ionized gas disks of IC 2233 are clumpy and vertically distended , with scale heights comparable to that of the young stellar disk . Both the stellar and H i disks of IC 2233 appear flared , and we also find a vertically extended , rotationally anomalous component of H i extending to \sim 2.4 d _ { 10 } kpc from the midplane . The H i disk exhibits a mild lopsidedness as well as a global corrugation pattern with a period of \sim 7 ~ { } d _ { 10 } kpc and an amplitude of \sim 150 ~ { } d _ { 10 } 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 ^ { \prime } \hskip { -4.836969 pt } . \hskip { 0.0 pt } 7 from IC 2233 , NGC 2537 has an H i disk with a bright , tilted inner ring and a flocculent , dynamically cold outer region that extends to \sim 3.5 times the extent of the stellar light ( D _ { 25 } ) . Although NGC 2537 is rotationally-dominated , we measure H i velocity dispersions as high as \sigma _ { V, HI } \sim 25 km s ^ { -1 } near its center , indicative of significant turbulent motions . The inner rotation curve rises steeply , implying a strong central mass concentration . Our data indicate that IC 2233 and NGC 2537 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 IC 2233 or NGC 2537 , suggesting that both are examples of small disk galaxies evolving in relative isolation .