The Scotsman approached Mr Stevenson with questions about whether his shareholding breached the ministerial code of conduct. The SNP government spent most of yesterday rejecting any suggestion of a conflict of interest and defending Mr Stevenson's right to continue holding the shares while dealing with ScottishPower as the transport and climate-change minister.
But by last night, and after a day of negotiation between Alex Salmond, the First Minister, his advisers and Mr Stevenson, the minister announced he would be putting the shares up for sale to avoid any perception of a conflict of interest.
Mr Stevenson eventually issued a statement at 8:20pm.
He said: "I know that there has been no conflict of interests, and I cannot see any likely conflict of interest in these shareholdings and general legislation. However, I am passionately committed to the climate-change legislation that I will be charged with bringing forward as a minister.
"Given that the ministerial code does speak about perception, I am disposing of all energy company shares to remove any scintilla of any possible conflict at any time in the future."
The furore over Mr Stevenson's shares started when The Scotsman approached the Scottish Government to ask whether the minister had placed his shares in a blind trust, whether he was going to sell the shares or whether he would absent himself from any discussions with ScottishPower in the future.
The company is one of the big players in the energy market in Scotland. It is heavily involved in traditional, coal-fired electricity generation, but it also has an expanding interest in renewable energy.
Just last week, Spanish-owned ScottishPower was given the go-ahead by the Scottish Government for a 200million wind-farm development in Dumfries and Galloway.
That decision was taken by Jim Mather, the energy minister, not by Mr Stevenson, who has a much wider brief - to put together the government's Climate Change Bill. That legislation will set new targets for a reduction in emissions and provide a big boost for renewables.
Reacting to Mr Stevenson's shareholding, Bob Graham, from the campaign group Highlands Against Wind Farms, said: "There is a clear conflict of interest here. He is going to make recommendations that are going to have an impact on ScottishPower.
"This government has to be seen to be squeaky clean. Its credibility is up for grabs."
Nicol Stephen, the leader of the Scottish Liberal Democrats and a minister in the last Executive, said ministers should not have any control over their own shares. "Ministers would normally sell their shares or put them in a blind trust. I hope that all new ministers will follow the ministerial code," he said.
The ministerial code of conduct states that ministers not only have to avoid any conflict of interest, but any possible perception of a conflict of interest.
The first passage of the section of the code dealing with conflicts of interest says: "Ministers will want to order their affairs so that no conflict arises or is thought to arise between their private interests (financial or otherwise) and their public duties.
"It is the personal responsibility of each minister to decide whether and what action is needed to avoid a conflict or the perception of conflict and to defend that decision, if necessary, by accounting for it in the parliament."
At first, a spokesman for the Scottish Government stressed the minister had held the shares for 20 years and that he had no intention of trading them or doing anything with them while he was a minister.
But, by last night, the government's message had changed.
A spokesman for the government then said: "For the avoidance of any scintilla of doubt, Mr Stevenson will now dispose of his shareholdings in ScottishPower, and also a small number of shares that he holds with SSE [Scottish and Southern Energy]. In addition, his wife will dispose of the same energy company shares that she has owned for the same period of time.
"This is his decision, as provided for in the ministerial code, and he has informed the First Minister and permanent secretary in writing.
"And furthermore, he repeats his existing position that he will not engage in trading of any other shareholding during his period of ministerial office."
The day-long wrangle over Mr Stevenson's shareholdings has clearly caused considerable problems for the Scottish Government in general, and for the First Minister in particular.
Last year, Mr Salmond put pressure on the Liberal Democrats' George Lyon, then Europe minister, to resign, over payments he received as a farmer from the European Union and which Mr Salmond believed represented a conflict of interest.
The First Minister is determined that his government does not fall prey to the same sort of problems that have plagued other governments: conflicts of interest and distrust from the public, which is why he came to the arrangement with Mr Stevenson to end this particular story as quickly as possible.