Have a 1 lb round steak.

I like to cook round steak with onions, green and red pepper, garlic, paprika and tomato sauce and serve it over mashed potatoes. Sear the steak first and then saute all the rest with it..let it simmer in the tomato sauce until tender.

Flatten it out and cut into two portions. Put it in plastic wrap and smack it with a rolling pin a few time. Or better yet use a 'needle tenderizer'.
Make a country fried (chicken fried) steak.
Dust with flour, then eggwash, then flour, eggwash, flour.
Fry and serve with a white creme gravy seasoned with finely ground black pepper.
I highly recommend the needle tenderizer. (Jacquard Tenderizer).
It can turn round steak into a quick cooking tenderness.
http://www.amazon.com/gp/product/B001347JK6/ref=pd_lpo_k2_dp_sr_1?pf_rd_p=486539851&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=B002TOKH3K&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=11710FCW6RYS3499K0HT

Beef jerky would work, you can always slow cook it will be tender.

Maybe I'll make beef jerky outta it. :-D

You might still have to do some chewin' pardner, but with a tough piece of meat the general rule is cook it till it hollers uncle. Google yourself a Swiss steak recipe and simmer, or crock-pot the stubborn critter overnight.

I made this recipe for flank steak but I think would translate nicely for round, maybe give it a few whacks to tenderize a bit but you can sear and finish in the oven quickly after a marinade and it would be delicious.
http://www.food52.com/recipes/13349_flank_steak_on_texas_toast_with_chimichurriHere is another great recipe and a round steak would be fine:
http://www.food52.com/recipes/10252_sugar_steak_with_bourbon