Abstract. In this paper we obtain parameterized subexponential-time algorithms for p-Kemeny Aggregation (p-KAGG) -a problem in social choice theory -and for p-One-Sided Crossing Minimization (p-OSCM) -a problem in graph drawing (see the introduction for definitions). These algorithms run in time O * (2, where k is the parameter, and significantly improve the previous best algorithms with running times O * (1.403 k ) and O * (1.4656 k ), respectively. We also study natural "above-guarantee" versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions are equivalent to a weighted variant of p-Directed Feedback Arc Set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of "votes" in the input to p-KAGG is odd the above guarantee version can still be solved in time O * (2 O( √ k log k) ), while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails (equivalently, unless FPT=M[1]).