The Texans worked out veteran punters Ryan Allen and Matt Wile, according to league sources not authorized to speak publicly.
Allen got beaten out by fifth-round pick Jake Bailey.
Allen has a career 45.3 average over the past six seasons with the New England Patriots.
Wile was waived by the Minnesota Vikings as the team signed Britton Colquitt.
Wile averaged 45.3 yards per punt last season.
Trevor Daniel remains the Texans' punter after beating out Bryan Anger in a preseason competition. He averaged 43.7 yards as a rookie after going undrafted out of Tennessee.