I was puzzling over this problem recently as I have decided to get rid of forty-five years' worth of journals, some of them big thick A4 books, closely written (a lot of angst).
I tried shredding two of them which created a huge sack full of paper and anyway I didn't want to just dump it all in the tip because I am very fond of my journals and wanted to give them a proper send-off.
So I bought one of those garden incinerators which have been mentioned and burn the pages from the journals without shredding.
I was worried about smoking out the neighbourhood but we picked a night, last week, where there was absolutely no wind and I checked no washing was out (although windows were open) and went for it. A bit of smoke which went straight up and not across, which I thought was reasonable, certainly nowhere near as bad as a barbecue.