Then, to our infinite chagrin, we spotted a single hiker coming down the ridge from Ben Starav, a prominent peak to the north. His sky-blue anorak and white woolly hat with red bobble on it made him immensely conspicuous - but it was his smell, rather than his appearance, that caused chaos. Long before he came into the view of the deer, a whiff of his scent sent the stags hurtling away round the shoulder of the hill.
We never found them again. The hiker disappeared. He never saw us. He never saw the deer. He cannot have had any idea that he had ruined our plan and our day - but all we could do in the afternoon was trudge for home.
It was incidents of this kind, repeated a hundred times over and with ever-increasing frequency, that led eventually to the "Concordat on Access" to the Scottish hills which was ceremonially signed last week at Battleby, near Perth, the headquarters of Scottish Natural Heritage. So contentious is the whole subject that meetings had been going on intermittently for nearly two years, and the paper passed through eight drafts before everyone was satisfied with its wording. Several of the participants - ramblers, mountaineers, farmers, deer-forest owners, local authorities - reckon the Access Forum would have foundered but for the exceptional diplomatic skills of Magnus Magnusson, Chairman of SNH, who directed proceedings.
The Concordat rings with phrases designed to promote tolerance on all sides. Freedom of access to the hills should be "exercised with responsibility"; visitors must accept "the needs of land management" and "have respect for the needs of livestock and wildlife"; land-managers must recognise "the public's expectation of having access to the hills".
One aim of the agreement is to defuse the confrontational attitude of organisations such as the Ramblers' Association, which have tended to regard the deer-forest owners as the enemy. In a way such antagonism has been inevitable, for the red-deer ground covers a vast range - some six million acres of open hill, and nearly two million of plantations - and encompasses most of the Highlands.
The paramount need of the owners is to cull their herds efficiently so that they can keep numbers to a level which the environment can sustain. It is thus vital to them that in the culling season - autumn and early winter - their ground is disturbed as little as possible. On the other hand hikers and mountaineers do not see why they should be barred from land that is apparently open to all.
The answer, of course, is compromise. The owners now accept that they must provide more information. Notices beside paths, warning visitors that stalking is in progress, will be friendlier and fuller than in the past. Leaflets explaining when, where and why culling has to take place will be made available in information centres, hotels and pubs. Another idea is to set up an efficient hill telephone service, with answer-tapes saying which areas will or will not be safe during the next 24 hours.
The owners naturally hope that visitors will respond to such initiatives and realise that "factors other than their own enjoyment also have importance". They know that the Concordat is a fragile agreement, not supported by law; but they prefer a voluntary solution of their problems to a legal one, and now, as Mr Gibbs puts it, they "very much hope that everyone will join in to make it work".