Oversampled pyramid decompositions have been successfully applied to scalable video coding. Quantization noise feedback at the encoder ("closed-loop coding") has several advantages compared to "open-loop coding" where noise feedback is not included. Finding optimal bit allocations for closed-loop coders is a complex task since the rate-distortion (R-D) performance of one quantizer depends on the selected operational points of all previous ones. We present simplified models for closed-loop and open-loop coding. From those, analytical solutions to the optimal bit allocation problem can be derived. In the optimal case, closed-loop coding outperforms open-loop coding although distortion in lower resolution layers of the closed-loop coder may become rather high which is undesirable in scalable coding applications. In this case it turns out to be a good solution to use an optimal open-loop bit allocation for closed-loop coding. Theoretical results are verified by coding experiments.