Comparing magnitudes of logit/ordered logit coefficient estimates


I have a logit model with a number of independent variables which are binary and therefore measured on the same scale. I am stuck on what seems to be a fairly basic/straightforward issue.

First, while I am aware that a direct comparison between the coefficient estimates should not be performed due to scaling issues, I wonder whether it could be done in this particular case (i.e., when the dependent variables are all binary).

Second, could someone advise me on a procedure for assessing the relative importance of coefficient estimates for two different regressions. I need something like a variance decomposition method which would allow me to compare the importance of independent variables within the same regression and compare these results to those from another regression with a different dependent variable.

Thank you SO much in advance!!