Pillar is out of the lineup for the first game of Tuesday's doubleheader against the Nationals, Brendan Kennedy of the Toronto Star reports. Pillar started each of the previous 10 games, and the Jays planned to rest him for Monday's contest, which was ultimately postponed due to rain. Pillar will likely rejoin the lineup for the second game of Tuesday's doubleheader, against early Cy Young favorite Max Scherzer.