Mortgage Paid- Off Rental Properties-- Good strategy?

[Michael Davis]

We have 2 single family rental homes in California which have no mortgages.  Cash flow is relatively high since only property taxes and insurance are outgoing payments (and necessary maintenance/repairs).

The properties have been owned for about 5 years and have appreciated significantly (about 35%).  

The question is, should we mortgage these properties and use the cash to purchase additional investments?  A mortgage would lower our cashflow, but potentially allow for additional rental properties.  We are both retired and mainly use the cash flow for international travel.  Additional properties would mean even more time invested (or a management company).

What is the general thought on mortgaging a paid-off rental property?  Good investment idea?