Geez, what did you do, cross-post this to slashdot?
Now that the Ian’s website is back up, this describes the problem and the solution very clearly.
If your tied bow lies across your foot, you’re solid. If your bow lies ankle to toe, you’ll be retying shortly.
Round, eh? That does pose a problem. Still, a single snip with a good pair of scissors should bring things back into order, shouldn’t it?
Double knots, people. Sheesh. Tie your shoes as per normal, then, take the two loops and yank a simple overhand knot. It never comes untied. I use this habitually, whether running, hiking, walking around, caving, whatever.
And you don’t have to learn a new knot.
Thanks for this. I was reading this website with a growing bewilderment thinking, but the flat shoelaces were the ‘new’ style.
Not just round, but with a twist in it. Mobius strip laces confound me.
I used to have my shoelaces come untied all the time, until I realized I was tying a sort of granny knot. Try this: when you’re tying the last part, cross the bows over the other way (from the way you’re currently doing it).
I retrained myself and my shoes stay tied all the time. Independent confirmation: My friend God of Citroens, whom I retrained to tie his shoes properly, thinks I’m a genius.
A lot of my real shoes only have openings for round laces, not flat ones. Those few that come undone, I do a normal knot after the lace knot. But It’s interesting to see other knot possibilities.
Yankz, my friends.
<cynical laugh>
I used to think that, until both DogDad and I got new shoelaces. I’d hassle him for not knotting his laces after tying, because his were always coming undone. Finally he got pissed and said, “fine, YOU do it for me then.” I tied his laces, did the overhand-knot thing with the loops, pulled them as tight as I could.
I swear to you, fifteen minutes is all it took for those damn laces to untie themselves.
I’ve emailed him Ian’s solution and I’m hoping it works.
I think it depends on the material used to make the laces. I’ve had some round laces that stay put with a single, common bow knot, and others that come untied when you look at them sideways. The laces on the shoes I’m wearing today are round and they stay put. The laces on my daughter’s sneakers, even when her mother or I tie them, come untied 4-5 times a day.
That’s interesting. It took me a couple of goes at tying my laces in slow motion but I eventually figured out that I tie a good knot and probably always have done. I was a bit bemused at all this talk of laces coming undone.
One word: velcro
Oh, oh, oh, a chance to plug the best thing to set foot in the world of accessories in the last decade:
“Bubble” Sure-Lace Laces. Or check out the video.
Got a pair as a gift a few years back and now I put them on every pair of shoes. They fucking work wonders, no new knots required.
Keeping your shoeslaces tied is easy. Just put a drop of glue on the knot. (No, not Gorilla Glue. That blue Children’s Glue that dissolves in water.)
Wow, thanks for that. I need some of those for my skates. Tripping over a shoelace is embarassing. Skating over a skate lace (and falling immediately flat on your face) is painful.
It’s great. 
I don’t know why a mild rant about shoelaces pleases me so much, but it does.
BTW, yore means ‘long ago.’ I didn’t know they had vaccum tubes in the days of yore. The Straight Dope - you learn something new every day!
I am going to start a related thread in MPMSIMS about when you learnt to tie your laces.
Great! Now your shoes will only untie at the worst possible time - when you’re walking outside in the rain 
The only reason I can see for using velcro instead of proper laces is either for children too small to tie a normal bow-knot (and at age kindergarten, they should start learning and practicing it), or for elder/handicapped people.
If you’re a real adult capable of tying knots, wearing grown-up shoes for real activities like walking or any kind of sports, laces are far better at adapting to your individual foot shape than one or two velcro bands.
I agree with this - while special knots help avoid problems, sometimes, the material is so slick that they come easily untied (mostly city shoes that have to look nice). In that case, maybe buying plain cotton laces and swapping the slippery laces, in addition to special knots, might help.