Check out this site

http://english.franklang.ru/35/

The Russian version of the site is much more impressive, containing around 30 languages, each with around a dozen texts on average.

Its a sentence by sentence literal translation of a text, then it repeats without the translation,
its quite an effective method, try one story and see if you pick up anything.
The idea of it is to save you time from having to look up every word you don't understand or having to find the correct accent center.

Unfortunately the selection for English speakers learning Russian is rather sparse, but you can also use the section for Russian speakers learning English with the loss of accent marks of course (not a problem if you have alphlex tho) the selection is MUCH more interesting and abundant from this perspective.

(click one of the free texts with the words "скачать бесплатно")
http://www.franklang.ru/620/


Bilingual texts (not sentence by sentence translation)
http://www.franklang.ru/626/


On a side note I like to use the section for Russian speakers learning Spanish, its great for the whole two birds one stone thing. The gaps you have in either language will fill each other in, its really helped me with both.

Check it out.