SAN FRANCISCO -- The Giants didn't wait long this week to keep the roster moves coming.

They claimed right-hander Burch Smith off waivers from the Milwaukee Brewers on Monday, with reliever Ryan Dull -- picked up last week -- getting designated for assignment to clear a roster spot. Smith was assigned to Triple-A Sacramento, where the Giants previously had Dull, Kyle Barraclough (also picked up last week) and Carlos Torres (signed last week).

Smith is the latest to get added in search of relief depth. The 29-year-old had a 7.82 ERA in seven relief appearances for the Brewers but was 6-3 with a 2.33 ERA in 15 starts for their Triple-A affiliate in San Antonio.

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Smith had previously made 10 appearances for the Padres in 2013 and 38 for the Royals last year. He has experience starting and relieving and has averaged 9.7 strikeouts per nine innings as a big leaguer.

The Giants also optioned Conner Menez, who struggled Sunday night, back to Triple-A. They will add a player before Tuesday's game against the A's.