Several methods have been proposed for imaging biological tissue structures at the near micron scale and with user-control of contrast mechanisms that differentiate among the tissue structures. On the one hand, treatment with high-Z contrast agents (Ba, Cs, I, etc.) by injection or soaking and absorption edge imaging distinguishes soft tissue from cornified or bony tissue. This experiment is most compatible with high-bandpass monochromators (ΔE/E between 0.01 - 0.03), such as recently installed at the LSU synchrotron (CAMD). On the other hand, phase contrast imaging does not require any pre-treatment except preservation in formalin, but places more demands upon the X-ray source. This experiment is more compatible with beam lines, such as 13 BM-D at APS, which operates with a narrow bandpass monochromator (ΔE/E ≈ 10-4). Here, we compare imaging results of soft, cornified and bony tissues across the 2x2 matrix of absorption edge versus phase contrast, and high versus narrow bandpass monochromators. In addition, we comment on new data acquisition strategies adapted to the fragile character of biological tissues: (a) a 100 % humidity chamber, and (b) a data acquisition strategy, based on the Greek golden ratio, that more quickly leads to image convergence. The latter incurs the minor cost of reprogramming, or relabeling, images with order and angle. Subsequently, tomography data sets can be acquired based on synchrotron performance and sample fragility.