Before I book via sidestep.com want to check the wire to see if I can go cheaper!
Is $335 a good deal Budapest to Tallinn?
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Have you tried multiple flights? For example, you can find flights from Tallin to Brussels, and presumably the reverse for 65€. If you can find a similarly cheap flight from Budapest to Brussels, it would seem that you would save money--but be careful, because some cheap flights are advertised without the additional fees and taxes that can double the price.
You did not post the dates you need, but there are many other possiilities that you won't see on sidestep.com.
There are many European LCC airlines that are not listed on any major travel site.
My suggestion is to go to www.whichbudget.com and try to work your itn through Copenhagen. Sterling airlines will get you there from Budapest for about $100 and you could connect to Estonian Airlines for as low as $50.
Just make sure you have enough connection time. The LCC fares are low, but they also do not protect you if you miss your connection. You can't check through, so you will need to check n again in Copenhagen.
It's basicaly the same suggestion as above, but there is really no need to fly back to Brussels. Copenhagen connection will save you time and maybe some $ as well.
Good luck!
When using whichbudget.com, the trick is to give Tallin as your departure point to find out which other cities are connected to it with which airlines, and then see if the reverse flight is within your financial and scheduling ball park.