The 79th annual appeal opened in November and runs through February.
But he expressed concern over those times Voy acknowledged positive tests before the appeal had run its course.
The fund's 85th annual appeal, now under way, runs through Feb. 28.
But in many instances counsel comes only after execution dates are set and before routine appeals have run their course.
The fund's 84th annual appeal for donations runs through Feb. 29.
Critics question whether the company has any incentive to settle now instead of letting further hearings and appeals run their course.
The fund's 85th annual appeal runs through the end of the month.
Such appeals in a political context, the league said, risk alienating people and also run "contrary to the American ideal."
The 76th annual appeal, which started after Thanksgiving, runs through February.
The pace of executions climbs as appeals run their course.