Narrative:

I think sector X was red - or close to it - during our noon push. I was also handling multiple deviations for weather. Our staffing is low; so we did not have a D side at the time to offer me and our supervisor was in recurrent training so we had a controller in charge on the desk; taking one more controller away from the floor. I felt busy - I descended aircraft X from FL410 to FL390 to start stepping him down through all my traffic. I think I was busy enough that I don't remember the read back. I continued working on other things and saw conflict alert go off as the aircraft X pilot asked me if he had traffic. I said yes - and told him I thought I had cleared him to FL390 - he said he answered with FL290. He was a few miles - maybe 3.5 miles lateral from aircraft Y at FL380. I saw more traffic for him at FL360 so I reissued his clearance to descend to FL370. He repeated FL370.we need better staffing. We shouldn't be allowing controllers or supervisors to attend classes when we are 1 below the minimum safe number of controllers at the start of the shift. If I had a second pair of eyes or ears; maybe they would have caught it. I haven't listened to the falcon; but I probably did miss his read back. I don't know.

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Original NASA ASRS Text

Title: Denver Center Controller and corporate pilot reported a loss of separation due to communication error with pilot and ATC.

Narrative: I think Sector X was red - or close to it - during our noon push. I was also handling multiple deviations for weather. Our staffing is low; so we did not have a D side at the time to offer me and our supervisor was in recurrent training so we had a CIC on the desk; taking one more controller away from the floor. I felt busy - I descended Aircraft X from FL410 to FL390 to start stepping him down through all my traffic. I think I was busy enough that I don't remember the read back. I continued working on other things and saw conflict alert go off as the Aircraft X pilot asked me if he had traffic. I said yes - and told him I thought I had cleared him to FL390 - he said he answered with FL290. He was a few miles - maybe 3.5 miles lateral from Aircraft Y at FL380. I saw more traffic for him at FL360 so I reissued his clearance to descend to FL370. He repeated FL370.We need better staffing. We shouldn't be allowing controllers or supervisors to attend classes when we are 1 below the minimum safe number of controllers at the start of the shift. If I had a second pair of eyes or ears; maybe they would have caught it. I haven't listened to the FALCON; but I probably did miss his read back. I don't know.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.