Book Recommendation for Microeconometrics of Discrete Data I am looking for a few good books pitched at different levels to help analyse discrete data.

Specifically: Specification, Estimation and the application of econometric methods to model discrete choices by individuals, households or firms.
Personally, for choice analysis, I like


Discrete Choice Methods with Simulation by Ken Train (pdf)
Applied Choice Analysis: A Primer by Hensher and Greene (2nd edition, book)
Modeling Ordered Choices by Hensher and Greene (pdf)
Regression Models for Categorical Dependent Variables Using Stata by Long and Freese (3rd edition, book)


(1) is a fairly short, readable classic. (2) is much more introductory, with lots of intuition, though it devotes a lot of space to the nlogit software. (3) has the same features as (2), but for a more focused set of topics. (4) is also pretty introductory and focuses on using Stata. It is perhaps the least "economisty" of the four, but still quite good.

For count data, I like Cameron and Trivedi's count data book, followed by Winkelmann's.

The books you have listed are good, particularly Wooldridge, but they cover much more ground than just discrete data at the expense of depth.