How can I get rid of what remains of a childhood speech impediment?

Though I have never lived outside of America, people pick up on what they perceive as an accent from me. They tend to think I am Irish, Scottish, or Russian. When I ask these people why they believe I have a foreign accent, they most often mention how I pronounce the letter R, and vowels. If this was a genuine accent on my part, I would have no problem with this, but this almost certainly is a remnant of a speech impediment I had as a kid. Though I conquered this issue to the satisfaction parents and speech therapist, I obviously did not conqueror it fully. When I try to copy how someone pronounces a word, I believe I do so perfectly, but others hear clear differences. This must be a problem of perception more than motor skill on my part making practicing imitation rather pointless. I admit this issue is rather harmless, and this is why it has not been a huge priority for me. I am however a little self conscious about it and would consider it a huge victory if I can get over this completely.