Claiming expenses - shooting yourself in the foot?

I have been contemplating whether or not to claim all my expenses. If I claim, for example, $3,600 in expenses, I might pay around 6-800 less in taxes. However, come time to apply for a new loan, I will show $300/month less in rental income consideration toward my DTI ratio. Anybody here not claim expenses or not all expenses to better qualify for more mortgages?

Also, for those familiar with underwriting, does the bank count depreciation against rental income as it does expenses when analyzing the Schedule E?