Stepwise Logit Regression - Drop of variables

Dear All,

I have a small question I hope you could help me with.

I am trying to find a predictive model for a dataset doing a stepwise logit regression.

I have a few variables with info that is included in another variable. E.g. "income" (0-9 with 0=income is missing) and "income missing" (dummy with 1= missing).

My understanding would be to drop variables such as "income missing" before doing the stepwise logit regression, would that be the right way to do?

It just seems like it makes the model worse?

Many thanks!!!