His Hawick team-mate Hugh McLeod said this of Stevenson: "He was a like car. He had gears and he would move into top gear when he thought it was necessary. He was never happy touching the ball down in the corner. He would always want to touch down under the posts. He was such a character."[2]
He also played for the combined Scottish Districts side, notably in their 1965 match against the touring South Africa international side. Scoring a side-stepping try against the Springboks he helped the Scottish Districts side record a 16-8 win.
The Border Telegraph notes: "Everyone in Hawick that day knew that "Stevie" would sidestep because that was his routine in club colours. The only exception was the poor Springbok defender who was completely bamboozled."[2]
The Glasgow Herald noted the try as a 'spectacular solo try'.[4]
International career
He was capped 24 times for Scotland.[5] He scored a try on his debut against England.[4]
He trained to be an engineer but after his national service switched to working in food and drink production. He worked in Bibby's, an agricultural foodstuffs production before switching to be a representative for Ballantine's whisky.[4]