Chandra X-Ray Observatory (CXO) images have revealed that the X-ray-emitting regions of the moleculerich young planetary nebulae (PNe) BD +30 3639 and NGC 7027 are much more asymmetric than their optical nebulosities. To evaluate the potential origins of these X-ray asymmetries, we analyze X-ray images of BD +30 3639, NGC 7027, and another PN resolved by CXO, NGC 6543, within specific energy bands. Image resolution has been optimized by subpixel repositioning of individual X-ray events. The resulting subarcsecond resolution images reveal that the soft (E < 0:7 keV) X-ray emission from BD +30 3639 is more uniform than the harder emission, which is largely confined to the eastern rim of the optical nebula. In contrast, soft X-rays from NGC 7027 are highly localized and this PN is more axially symmetric in harder emission. The broadband X-ray morphologies of BD +30 3639 and NGC 7027 are highly anticorrelated with their distributions of visual extinction, as determined from high-resolution, space-and ground-based optical and infrared imaging. Hence, it is likely that the observed X-ray asymmetries of these nebulae are due in large part to the effects of nonuniform intranebular extinction. However, the energy-dependent X-ray structures in both nebulae and NGC 6543-which is by far the least dusty and molecule-rich of the three PNe and displays very uniform intranebular extinction-suggest that other mechanisms, such as the action of collimated outflows and heat conduction, are also important in determining the detailed X-ray morphologies of young PNe.