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FIRST & FOREMOST,.....Get that cat outta there! Big NO-NO! Cat's kill more birds each year (Pigeons Included) than any other predator in our quiet suburban city neighborhoods.

They should be given @ Minimum 3 Weeks, Provided they have a good view of the garden area you'll be letting them out into. You could slowly start in the second week but only if you do it early evening..say about the last hour of the day--before the sun sets! To do this open the door & gradually let them come out on their own & explore right outside the doorway, close to their home. Be Cautiouse that nothing scares them up into a panic @ this time tho, cuz it'll be hard to get them to come back down & in. Maybe you should gradually coax 'em outside the door in the evening with a sprinkling of food or you could just let ONE bird out @ a time, being sure that the other is inside the house in full view for the one outside to be able to see it. Gradually it'll work out & they'll come to know their home .! Good Luck with them.

homing "PIDGIONS" need to be homed for three weeks, Doves are tamer so Id say two - three weeks should be enough.

You will be lucky.