"In Rome my expectations weren't that high. My personal goal was to make the final, for all [legendary coach] Arthur Lydiard might have said," Snell said of his coach who was fond of talking up his man. "That was total elation, suddenly transformed from someone unknown, 25th in the world, to gold medalist.
"By the time Tokyo came around, anything other than gold medals would have been very disappointing."
But was attempting the 800m-1500m double always part of the thinking? As defending champion in the shorter distance, it would seem logical he would contest that.
However, by 1964 he had not run many more races over that distance after 1962, the year of wondrous achievement, when he broke the world mile mark on grass at Wanganui's Cooks Gardens, the world 800m and 880 yards in one race at Christchurch's Lancaster Park - grass again - and did the 880 yard-one mile double at the Perth Commonwealth Games.
Plus there was another runner called John Davies who was giving the champ some real competition. Time to prepare...
Leadup
"John was emerging as a real threat and beating me, so I had to get out of the country to get a few victories," Snell recalled with a chuckle.
He went to South Africa, ran "quite well" over 800m and completed the first four-minute mile in the country, in Cape Town early in 1964.
Confidence restored he went home and got into total preparation mode. However, there was a hitch. New Zealand tracks back then in midwinter, mud and slush, were far from ideal.
Snell remembers training at Alexandra Park and in a 10-week period clocked up around 1010 miles, reaching the magic 100 miles a week.
The team stopped off in Australia en route to Japan and he got in a race there. Arriving in Tokyo Snell felt in top shape.
"Tokyo was characterised by my best winter training in New Zealand.
"It turned out to be one of the best conditioning preparations I'd had."
He knew, coming out of a New Zealand winter, he needed a couple of races under his belt before the heats of the 800m. Australia helped, but so did a pre-Games 800m trial arranged by Lydiard.
Snell remembers it vividly 50 years on.
"When we got to the Games and started doing faster training on the track, it was necessary to do races amongst ourselves.
"That race was highly significant. I ran 1min 47.1s, a world-class time and under true race conditions. That made me realise the double was on.
"But I was worried about 'am I trying to do too much?' The double involved six races in eight days. The 800m came first. What say I didn't win that, then found myself struggling to do well at 1500?
"It turned out that my toughest day was qualifying in the 1500m, the day after the 800m final. Then I had a rest day and that was all I needed."
The 800m
Snell turns to shake hands with Wilson Kiprugut, right, of Kenya as Bill Crothers, left, of Canada watches during the 800m medal ceremony. Photo / AP
Snell believes the 800m final to be one of his finest performances. He won his semifinal in 1:46.9, however the classy Jamaican George Kerr set an Olympic record, 1min 46.1s, in the other semi. The challenge had been thrown down.
"I rated George highly. He was so much faster over the shorter distance," Snell said. "He could run 46s for the 400m. My best was around 48s so my task whenever I raced him was to make sure the pace was fast enough so he was too tired to use his superior sprint speed at the end."
In the final, Snell had to think swiftly on his feet. He found himself completely boxed in for more than a lap.
"There were runners in front of me. I literally had nowhere to go. I had to drop back to the end of the field, then go round into a challenging position.
"I'd got there by the end of the back straight, then had to make my winning move. It was essentially two surges - one to get into position, one to try and break the field."
He held off the bespectacled Canadian Bill Crothers and graceful Kenyan Wilson Kiprugut. It was Snell's third race in as many days - heat, semi and final - and he ran 1:45.1, breaking Kerr's Olympic record of 24 hours earlier.
Indeed the first four runners all eclipsed the old Olympic mark.
The 1500m
Snell on the winner's podium after the 1500m race, with silver medalist Josef Odlozil of Czechoslovakia (left) and fellow Kiwi John Davies. Photo / AP
The second half of Snell's double began with heats the following day.
He finished third, quite deliberately doing enough to qualify without overextending himself.
Then came a rest day and that was all he needed.
The semifinal was won, but it was a tight squeeze in the other semi for Davies.
"It was very close, but he must have more of something because he ran so well in the final, in spite of having to lead for a fair chunk."
In the final, just after the bell rang signalling the final lap, trouble loomed.
Traffic was building up and Snell found himself once more stuck inside.
"I thought 'I'm not going to go to the back of the field again. I'm going to get out of here'."
The Briton John Whetton was outside Snell. When the big New Zealander put his right arm out, as if signalling a turn on a bicycle, Whetton duly moved to his right and Snell was clear.
Race, effectively, over.
Snell gave his familiar surge, his arms characteristically riding low, powerful legs driving hard. By the turn, once he checked behind him, he knew the race was his. The time, 3:38.1, was three seconds off Herb Elliott's world record of 3:35.6, set in Rome in 1960.
Didn't matter.
Behind him, Czech runner Josef Odlozil pipped another black singlet for silver. Davies won bronze. The two New Zealanders were first and second at the Perth Commonwealth Games two years earlier. This was better. Snell was chuffed.
"Getting up on the dais for the flag raising, that was a real special moment. It felt like we had a degree of domination of this event. This was a bigger stage [than Perth] and it felt really good.
"To me it's much better than it if was just a solo thing."
The only other athlete to complete the 800-1500m Olympic double is Englishman Albert Hill in 1920.
The aftermath
Snell takes gold in the 1500m Olympic final in 1964. Photo / Herald archive
Within a year Snell was gone. Just as Bjorn Borg departed tennis at 26, so Snell walked away at the same age.
From this distance, considering his pre-eminence at the time, it seems almost bizarre.
However, Snell now admits he had made the decision to stop three years earlier.
"When I ran those times [in 1962] I psychologically told myself 'you've made it, you've achieved this and there's only one place to go from here', and that was down.
"I would do another two years to reinforce my standing in these events by showing I could do it again in Tokyo, and that would be it."
To make sure he would not change his mind, he did his biography with Garth Gilmour. That would disqualify him from running.
So does the Snell of 2014, now 75, ever regret that decision?
"Sometimes I feel a bit wistful about it. If I could have gone on another four years I would have been young enough to have done well at the 800m. It would have been really good to have won the 800m three times.
"The time in Mexico City [1968 Olympics] wasn't particularly fast and it's the last event where I think you can benefit from high altitude. The 1500m is more of a problem."
Having said that, Snell remembers the sacrifices. Working a standard day job, then training in the evenings would have been hard to sustain.
"And I had other ambitions. I was married by this time, wanted to start a family and enjoyed other pursuits. For me, running was not a No 1 sport; it just happened to be the one I was best at.
"It was a vehicle to satisfy my need for achievement. I'm happy to admit that now.
"My background was ball games. I was brought up on tennis, cricket, I liked badminton and golf. They were games I enjoyed more than running. But what I enjoyed about running was the success."
Still, three golds has a nice ring to it.
"Occasionally I think 'darn that would have been really nice'," he laughed.
"But then I say, well so what. What I'd have had to go through. So no, I feel comfortable with the way it's worked out."
App users: Tap here to watch 'Mens 800m and 1500m Tokyo highlights'
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10 of his finest performances
Sept 1960
Peter Snell breaks the Olympic record and stuns the athletic world in winning the 800m final in Rome.
Jan 1962
Running on grass at Wanganui's Cooks Gardens, Snell sets the world mile record, running 3min 54.4, shaving a 10th of a second off Australian legend Herb Elliott's record.
Feb 1962
Snell grabs world 800m and 880 yard records in one race, at Christchurch's Lancaster Park, also on grass, clocking 1:44.3 for the metric distance, just eight days after the Cooks Gardens race.
Nov 1962
Snell wins a tough 880 yards Empire Games final in Perth, after a thrilling battle down the home straight with Jamaican George Kerr.
Nov 1962
It's a 1-2 finish for New Zealand in the mile final in Perth, with Snell heading home fellow Kiwi John Davies.
May, 1963
A burst 200m from the finish gave Snell a spectacular win in the Modesto mile in California, clocking 3min 54.9s against a field of Americans team racing to try to take him down.
Oct 1964
Snell breaks the 800m Olympic record again, in Tokyo, in a performance he rates among his most satisfying.
Oct 1964
Five days later Snell completes the Olympic middle distance double in Tokyo, winning the 1500m final, still one of only two men to achieve the feat.
Nov 1964
Snell sets world 1000m record, at 2:16.6, at Western Springs.
Nov 1964
Five days later, he eclipses his world mile mark from two years earlier, at Western Springs, in 3:54.04.