Our earlier daily Mass is at 6:45, and--at least when I celebrate it--it's over by 7:10 or so. The next liturgy is Morning Prayer, which isn't until 8. There is almost always some part of the empty, in between hour in which I can be found around the church and sacristy, either tidying up after the first Mass, setting up for Morning Prayer and the second Mass, or just getting started on my rosary for the day.
A handful of people have discovered, over time, that this is a time when they can go to confession. Of course I'm happy to hear their confessions, and at that time of the day I still have the energy to gratefully receive the opportunity of penance if I happen to be inconvenienced by them. They are almost always very brief encounters, little snippets of the larger and deeper conversation between an individual soul and the Lord.
I always laugh inside a little bit, though. I would never have done such a thing back when things were the other way around. Perhaps I'm just shy, but I didn't see priests as approachable enough to just ask for confession at a random moment. Even if I really felt it was time for a confession, I would wait for the regularly scheduled times.
I laugh because this is a good thing. Back in the earlier years of my Baptism I used to go to confession a lot; at least once a week for several spells. I still go at least once a month, and sometimes more often than that. But I protest that universal law instructs religious to approach the sacrament frequenter. (CIC, 664) I didn't always go to confession for the right reasons, though, and that's why it was providential for my to have been shy about approaching priests about it. Some of my frequent use of the sacrament was about contrition, for sure, and some of it was just because I had a lot of zeal and was working hard in prayer and interior asceticism in those years. But I also went to confession all the time because I was having a hard time accepting myself as a sinner. I only wanted to imagine myself as perfect, and so I would use the sacrament not so much to celebrate the forgiveness we have in Christ as to get rid of the sin that was interfering with my beloved idea of myself as so very devout. Holiness too can become an idol. "The devil is not afraid to preach the will of God, provided he can preach it in his own way." (Thomas Merton, New Seeds of Contemplation, 94)
So I'm grateful for the folks who interrupt my morning with their confessions; I'm just glad I didn't ever think to do such a thing when I was younger in the faith. I don't know if this is normal, but after my priestly ordination I was hearing confessions before I even offered my first Mass, and penitents continue to challenge me with their honesty and earnest devotion.