Before they selected Clemson defensive end Shaq Lawson with the No. 19 overall pick in the 2016 NFL Draft last night, the Buffalo Bills were on the phone with the Dallas Cowboys, attempting to trade down for a big haul.

Tim Graham of The Buffalo News reported the news late last night, after the first round had been completed. Buffalo had an offer on the table from the Cowboys, but they did not believe that Dallas was offering enough.

Cowboys called Bills to trade into No. 19 and draft Paxton Lynch, but offer wasn't good enough. — Tim Graham (@ByTimGraham) April 29, 2016

The Bills weren't the only team that Dallas called, either. ESPN's Todd Archer reported that the Cowboys offered Seattle second- and third-round picks to move up to No. 26 overall with Lynch still on the board, but that their offer was beaten out by Denver, who ended up selecting Lynch at that spot.

Cowboys offered Seahawks 2nd- and 3rd-round picks for their 1st to trade up for Paxton Lynch, per @toddarcher. Broncos' offer trumped it. — Adam Schefter (@AdamSchefter) April 29, 2016

What stopped the Bills from trading down from No. 19 to No. 34, and moving out of the first round entirely? According to Graham, it was the Cowboys' unwillingness to part ways with their 2017 first-round pick to seal the deal.