At the time of India's second round of nuke tests (post 1974); the doubts that were cast on the success of those tests was based wholly on a partial set of seismic data concerning blast force and propagation (through un-studied ground).
IN BRIEF: The doubters took their readings of the blast waves, and declared that the causative explosions were so small, that they constituted a 'fizzle'. They jumped to this conclusion, without the benefit of understanding the geology of the test sites, and without any baseline data that would concern simultaneous nuclear tests, which could conceivably generate interference patterns and unusual readings of the blast waves.
For their part, Indian scientists declared that the tests worked as expected, and doubts in this matter are based on a skeptical reading of that seismic data.
To set the doubters right; India had invited others to visit the site and draw their own samples, which would indicate the nuclear chemistry of a fusion reaction (lighter radio-isotopes). As to who took them up on this offer, I don't remember that, or even if it ever made mention in the press.
HOWEVER, this is all missing the point: India has tested 'smaller' devices, at least some of which have worked. As to what percentage of the fissile material was converted, and to that degree, how much of it was a 'fizzle', are basically immaterial from a strategic standpoint.
QUESTION: Has anyone doubted that India has achieved warhead miniaturization?
QUESTION: Is a small nuclear warhead (atop a very accurate, high speed missile), less of a deterrant than a much bigger warhead on a less accurate, slower missile?
ANSWER: NO (quite the opposite, really, since conceivably, smaller weapons are 'more useable' in that they have inherently less potential for collateral damage -- yeah, I do hate that euphemism, but you understand what I mean, I hope).
QUESTION: What if a large column of PLA tanks crosses the border -- What kind of nuclear weapon could be the best option, if nuclear arms are all that are available?
ANSWER: NOT a large weapon, but a small one, obviously, since it would be exploded over Indian territory. If this small weapon could be thermonuclear, the fallout hazzard would also be lessened, since the half lives of these expolsion byproducts is much less than with fusion weapons.
DON'T BELIEVE THE HYPE: India's nuclear deterent is taken seriously by everyone, except (it would seem), by large sections of the Indian 'chatterati'.
What's all this 'fizzle' fuss about? SELLING NEWSPAPERS!!!!! That's it.
BTW: Testing nuclear weapons in space is prohibted by international law, and it's a very bad idea for environmental reasons (damage to the ozone layer and ionosphere).
AND...... Splitting hairs is ridiculous, when it comes to nuclear warheads. Just for laughs, someone please explain to me the strategic (never mind, technical) difference between a 'fission-boosted fusion device' and a 'two-stage fusion device'.
What matters is miniaturization and accuracy in targetting. India has demonstrated this. These things are particularly important as techonological advances in ABM systems are foreseen, since it will always be a more devastating strategy to send multiple warheads to a single target, rather than one large warhead to that target. This should be obvious, on the face of it.
LASTLY, for further reading.... http://en.wikipedia.org/wiki/Variable_yield