Los Angeles Mayor Antonio Villaraigosa will announce his selection of the city's next police chief Tuesday, the mayor's staff said Sunday evening.

After summoning the three finalists for a second round of interviews Sunday, Villaraigosa decided to take an additional day to mull over the weighty choice. The mayor had tentatively planned to name his choice for chief Monday.

Los Angeles Police Department Deputy Chief Charlie Beck, Assistant Chief Jim McDonnell and Deputy Chief Michel Moore returned Sunday to Getty House, the mayor's official residence, to meet one-on-one with Villaraigosa for about an hour each. The candidates each met with Villaraigosa for several hours last week, and the mayor's request to see them again appeared to indicate that the choice was not an easy one.

Villaraigosa has said that picking the person to succeed William J. Bratton, who departed Saturday after seven years as chief, will be one of the most serious decisions he makes in office.

Beck, McDonnell and Moore each bring unique qualities and leadership styles to the table and would make very different chiefs. With the city facing a severe budget shortfall and general economic woes threatening to push crime higher, Bratton's successor will have the challenging task of continuing to make gains on crime rates -- or at least minimizing losses -- while keeping up morale among the rank and file.