Wy, these tings are just plain a nuisance-across a range of tree types. So what can be done? First, if one removes the suckers (when very new) via a twisting, tearing motion, rather than a nice neat cut with a hand pruners, it actually works better! But this must-as I've alluded to-be done before they get strong and stout. Then there's the matter of timing: Very basically speaking, suckers removed about mid-growing season will be much less apt to return than those removed early in the growing season. This will interfere with that other thing I said...there's no escape! But if one removes most of them early, via the twist-off method I mention above, then comes back later, say about mid-July, the one saving grace is that then you should be done with this task for the year.

I've got two Canada red cherries that I've often cursed for their proclivity towards basal and root suckering. But I've learned to manage, via the two factoids listed here.

If you don't mind chemicals, you could look into a Plant Growth Inhibitor such as Atrimmec.

cut them off, not much you can do. if you want another tree you can dig up the root and cut it (assuming it's not very close to the tree)

Yes, so-called Sucker-Stopper could be used, although I think that a bit heavy-handed for one or two trees. If this was a commercial setting, having dozens of such plants, i might consider the chemical route.

What is the species you are actually refering to?

Olea europaea? or Bucida buceras ?

Hmm, from Google Images I'd have to say it's Olea europaea. The chemical approach seemed ok except for two issues: 1. I'm afraid it would just kill the tree; 2: That stuff is EXPENSIVE! Guess I'm committed to hand picking sprouts for the rest of my life!

I took two sprouts from a golf course a few years ago and they rooted for me. We now have two nicely growing trees. I can't wait till they bear fruit, but I like the green olives best. I love to brine them, and jar them up with garlic, herbs and citrus. You need someone like me that wants the sprouts! :-)

Do not cut them, unless they are too big to remove as Tom instructed. Basically, ditto what Tom said.

I have a small olive tree (Olea) in a pot and those small branches are tough! They cannot be easily cut without a shears.

Never heard of sucker stopper. Would it work with crape myrtles? Buy where?

ETA I thought I'd read somewhere that moisture can encourage suckers, no?

Pricey! $47 a m Leonard

Consider yourself lucky, I have a hundred year old olive (Syrian type, sorry don't know the Latin name), shoots up these annoying sprouts at the rate of dozens each time. Since it is in my yard I tear off the new ones once a week, and every week they're back there at about 4-5 cm.