A top missile engineer, Professor Colby (Donald Churchill), has disappeared in Cyprus.  When news filters through that a Russian expert in missile guidance has also gone missing, it starts alarm bells ringing. Burnside, Laura and Willie kick around possibilities about who could have taken them.  In the end it seems that a group operating in Cyprus, such as the Greek Cypriot National Front, are the most likely suspects. Smuggling missiles into or out of Cyprus would be tricky – much better to have them prepared inside the country.

Another complication occurs when the deputy head of station in Cyprus is brutally killed. Logically, it makes no sense – until now it was only a theory that forces within Cyprus were responsible for kidnapping the scientists, but this murder seems to prove it. Burnside dispatches Caine to Cyprus and he’s accompanied by the replacement deputy, Jill Ferris (Sarah Bullen).

Wille’s not happy about minding a woman, but she quickly proves to be more than capable – which raises his suspicions, as she’s supposed to be fresh out of the training school. The answer is that she’s a Russian agent, who’s disposed of the real Jill Ferris (the Russians also killed the previous deputy head of station, so they could replace him with one of their own). Since the Russians only have a limited presence in Cyprus it makes sense for them to work covertly with the SIS. For now, Caine is told to play along with her – which may be a problem as he seems to find her somewhat attractive.

A Feasible Solution is a somewhat unusual episode of The Sandbaggers since it features quite a heavy amount of gunplay and plenty of dead bodies.  As soon as Caine and the bogus Jill Ferris arrive in Cyprus, they find themselves pitched into an intensive gun battle.  It’s interesting to hear Willie say that he doesn’t really like guns and Burnside comments that it’s the first time in over a year that Willie Caine has been armed.  Although he’s the chief Sandbagger, it seems that killing people isn’t something he particularly cares for – although he’s undoubtedly good at it.

Once again we see the UK doubling for a foreign country.  It works quite well here – thanks to the fact that the sun shone when the filming took place.  The soundtrack of chirping insects also helps to create the illusion of being abroad.  The missing scientists are almost a Macguffin, since the thrust of this part of the story is concerned with the relationship between Willie and Jill, as well as providing us with a more action-orientated episode than is usual.

Back in the UK, Burnside pays a visit to the section psychiatrist Philip Jeremiah (Richard Cornish).  Burnside tells him he’s convinced that Laura Dickens has some sort of hang-up and he wants to know what it is.  Jeremiah replies that she has no hang-up which will affect her performance as a Sandbagger, but there is something.  “She was dominated by her parents and told that all men are beasts, that sex is simply for the propagation of the species.”

The conclusion seems to be that Laura is very emotionally fragile. When Burnside asks how she would respond to kindness, say a dinner invitation, Jeremiah tells him not to try and hustle her into bed. “Incurable romantic” mutters Burnside in return. But he seems to have got the answer he wanted, and this is the clearest evidence yet that he’s interested in her as a person and not just as a Sandbagger.

Burnside and Laura have their dinner.  It’s another good scene from Marsden and Keen, with Burnside acting somewhat hesitant (a departure from his usual gruff, professional attitude).  When they return to his flat for a drink, she tells him that, given her past, he’ll have to be patient.  He replies that he can be, and the scene ends with Burnside laughing.  Which isn’t something you see every day!

By the end of the episode, he’s back to his usual, cold self though.  Caine has returned – and he’s managed to rescue Professor Colby.  The fake Jill Ferris also located the Russian scientist, Yugorov, although since he defected willingly she kills him.  Caine and Ferris go their separate ways, much to Burnside’s annoyance.  “You were alone with Colby and Yugorov whilst she made a dummy run with the ambulance. You didn’t think to put a bullet in Yugorov, blame it on the opposition? With Yugorov dead and out of the way, she’d have kept her cover and stayed on as the Cyprus number two and we could have fed her false information.”

A Feasible Solution is a good story for Ray Lonnen, as it allows us to see how well Caine works in the field.  It also develops the Burnside/Laura relationship – which is going to be resolved in the next story, which was also the final story of the first series, Special Relationship.