Morgan's are problems of plenty. "Good headaches", if you will. Having selected Stone, who can operate at around 145kph (90mph), as a like-for-like replacement for Liam Plunkett, who is absent for the first part of the series getting married, Morgan potentially has another good player whom he may have to disappoint when it comes time to pick a World Cup squad.
There are other excellent players in England who would make it to most other teams, he said, but whom England simply cannot pick in their XI right now, because the incumbents are just better.
"It is unfortunate, but when a side is doing well it tends to be the case that guys are sitting out who would be in any other team," Morgan said. "Due to the success of the team it's unfortunate they miss out."
It is too early to suggest just yet that Stone is deserving of a regular place in the England side, or even the squad, but his performance with the new ball in the second ODI seemed to suggest he could become an option at the World Cup. Stone frequently clocked speeds of above 140kph, and had several batsmen in visible distress.
His first international wicket, which came off only the seventh ball that he bowled, was pure fast-bowling theatre. He fired in a rapid bouncer at opener Niroshan Dickwella's throat. All the batsman could do was get his gloves in the way - mostly in self-preservation. The catch ballooned overhead to the wicketkeeper.
Morgan felt they may have found a bowler who could not only replace Plunkett if their first-choice quick was injured, but also brought something extra to the mix.
"To be honest there hasn't been a huge amount of depth in one position and that's replacing Liam Plunkett," Morgan said. "He's been phenomenal for us for the last few years and he went down in Australia and we found it very difficult to get a bowler with the same attributes - to bowl quick and change the pace of the game at any stage of the 50 overs.
"There were signs today suggest Olly could be one of those guys. Even taking the new ball gives him a new string to his bow. Liam doesn't really do that. I don't think you can disregard Olly from the World Cup based on today."
That Stone was able to settle into a good spell was partly down to the expert England had operating at the other end. Chris Woakes had already taken a wicket off the first over of the innings, and would claim two more before the Powerplay was out. Having missed the one-dayers during the England summer due to injury, it was a welcome return for the team's seam-bowling spearhead, who took 3 for 26 in his five overs.
"Woakes has been doing quite a lot, and goes overlooked a lot of the time," Morgan said. "He really set the tone, he made a relaxing impression early on for Olly to come in and do exactly what he does. Olly bowled exactly like he has in the nets and warm-up and that's a really good sign. He had pace, got the ball moving. It was all done with a calm head."