We design fair sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan \cite{CJ22}, who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality as in \cite{CJ22}. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from \cite{CJ22}.