Integrated circuits such as programmable integrated circuits may include programmable logic regions that can be configured to perform custom user functions. The programmable logic regions may produce output signals. The integrated circuit may include interconnects that route selected output signals throughout the integrated circuit. The integrated circuit may include output selection circuitry having output selection and interconnect selection stages. The output selection circuitry may be configured to select which of the output signals produced by the programmable logic regions are provided to the interconnects for routing. The interconnect selection stage may be formed using multiplexing circuits or tristate drivers. Logic design system computing equipment may be used to generate configuration data that can be used to program the output selection circuitry to reduce crosstalk by routing signals away from critical interconnects or by double-driving critical interconnects.