Specialness is a measure of the scarcity premium of procuring a specific security. We analyze the impact of security-specific supply and demand on specialness. After controlling for the auction cycle on the supply of the bonds, we show that specialness is higher for highly demanded bonds - in the repo and in the cash market - and for bonds with lower available supply. The ECB outright purchases provide a natural experiment to analyze the impact on the scarcity premium of a big buy-to-hold investor on bonds. We find evidence of both a stock and a flow effect of the purchases. These effects are amplified when purchases involve bonds already in high demand. The impact of the purchases on specialness is conditional on the amount of the same security already bought. Very special bonds have a higher probability to be underlying a fail-to-deliver transaction.