Because sidewalks are slanted for rain run-off, they pose a safety risk for baby strollers if the person pushing the stroller stops and doesn't apply the brake. If s/he releases the stroller's handle when the brake is not applied, the stroller may veer off towards the curb owing to gravity, wind, the baby's movements, traffic vibrations, etc. Not applying the brake when stopped is a common mistake. While parents may remember to apply the brake when stopped, other caregivers may not. Applicant's improvement provides fully automatic slip-clutch joining means to inhibit veering off by automatically coupling the stroller's rear wheels together when the stroller is stopped. When coupled, the rear wheels must rotate in unison thus helping to prevent the stroller from veering-off toward the curb. When the stroller is being pushed the slip clutch handily becomes disengaged by turning or making other course adjustments.