Street, who converted 35-of-37 save chances last season, suffered tightness and inflammation just before the Cactus League season opened. Street said head trainer Keith Dugger, in an effort to keep Street from pushing too hard, has scheduled him for an approximately 25-pitch bullpen session on Tuesday but hasn't made plans beyond that.
Street saw Sunday as a positive step, although how he feels Monday will determine how much progress he has made.
"I was probably letting it go 80 percent, which was a little better than expected," Street said. "My control was right there. I think I missed two spots out of 15.
"The big thing today was how does it feel coming off the slope [of the mound] and how will it feel tomorrow, after the little extra torque. We did a little eight workout, the first time in a while with the upper body."
Street said he hasn't felt pain in his shoulder at any point, just tightness.
Last Spring Training, Street managed 11 innings despite missing time in the middle with a hip flexor injury. Street believes he can get in nine innings. Street said he would like to have a two-inning appearance at some point to increase his sharpness.
Thomas Harding is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.