The increasing penetration of variable energy resources in modern electric power systems requires additional flexibility in ancillary service provision to maintain reliable and efficient grid operations. However, full recognition and appropriate compensation of this flexibility is difficult to ensure within current power market designs due to rigidities in service definitions and requirements. For example, reserve requirements (RRs) are typically set in advance at administratively determined levels. If RRs are too large, wasteful expenditures result; and, if RRs are too small, high real-time costs are incurred for peak generation and/or load curtailment. To address these problems, this paper proposes a new mixed-integer linear programming (MILP) formulation for the optimal clearing of a day-ahead market based on swing contracts and a dynamic reserve method permitting the daily adaptive updating of reserve zones. Numerical examples based on a 5-bus test system are used to illustrate the effectiveness of the proposed new day-ahead market design.