I'm not sure what difference "no line" makes as that is simply an aesthetic enhancement.

When the optician sets up the order, she should ask you where the line (visible or not) should be based on your lifestyle and use, plus the frame. My glasses are very narrow top to bottom so placement of that line was critical. For reading in bed or knitting, it's perfect. It sucks for the computer which is not only at a different height, it's also farther from my face. The optician should ask you all these questions, even down to going home and measuring the distance from your face to the monitor.

Therefore, computer-specific glasses were the way to go for me. Each one of us may be different.