Scientists think they can now explain the sequence of events deep inside the Earth that led to the major volcanic eruptions on Iceland earlier this year.
Using data from satellite radar, GPS, and seismometers, the group has sketched a blueprint for the "plumbing" underneath Eyjafjallajokull.
The analysis is published in the journal Nature.
It goes someway to explaining why the volcano caused so much disruption to European air traffic.
"We can say that each volcano has a plumbing system and with our observations we have come up with a model for the plumbing system that was active at Eyjafjallajokull during this whole event," said Professor Freysteinn Sigmundsson from the University of Iceland.
"We were surprised by how complex it was," he told BBC News.
The root cause of the eruptions was a major intrusion of magma below the mountain.
This was picked up in the middle of 2009 as a very subtle change in the shape of the volcano, detected at a GPS station.
It prompted Sigmundsson and colleagues to deploy a full array of instrumentation to track the mountain's behaviour.
This included tasking the German TerraSAR-X satellite to gather repeated radar images of the volcano.
From all of the data, the scientists believe they can describe how the intrusion fed the network of cracks and chambers inside Eyjafjallajokull.
They say the influx created two new sills which saw the molten rock spread laterally and begin to lift the mountain.
There were two eruptive phases - in March and April.
The team says the first phase resulted when the intrusion pushed up through a dyke to break the surface in a relatively calm manner just east of the summit on 20 March.
By that time, the volcano's flanks had expanded by more than 15cm (6in).
The eruption continued into April with a brief pause before a second and much more violent phase was initiated on 22 April.
This time, lava broke out through a new conduit under the ice on the summit of the mountain itself.
Contact between the molten rock and the ice produced an explosive cocktail, as water flashed to steam and gas escaped from bubbles in the magma.
It was this second phase which produced the huge "ash" plume that rose high into the atmosphere, disrupting air traffic over Europe for weeks on end.
The team says the violence could have been a consequence of the new intrusion encountering old and highly evolved magma left under the mountain from the last great series of eruptive events in the 1820s.
"When the second event started, we thought the interaction with the ice was very important - it produces fragmentation of the magma when it comes to the surface," explained Professor Sigmundsson.
"But fragmentation can also occur because gas is escaping from the magma. We think now most of the explosive activity was due to the composition of the [remnant] magma - its technical name is trachyandesite.
"That magma had more gas and it was more viscous, and this combination probably led to most of the explosive activity when it came into contact with the new magma.
"We say the ice-magma interaction augmented this explosivity."
Many have asked whether the eruption of Eyjafjallajokull could kick the nearby - and much larger - Katla volcano into life. However, the team says the plumbing systems under each mountain are separate and quite different in their structure.
It is likely, though, that Eyjafjallajokull will have lessons for volcanologists studying very similar mountains elsewhere in the world.
"There are many volcanoes on Earth that we can say are moderately active - they sleep for hundreds of years, or even longer times," Professor Sigmundsson told BBC News.
"Their reawakening may be similar to what we observed at Eyjafjallajokull. We have such detailed records - we have may be one of the best cases of observations of how a moderately active volcano wakes up and of the events preceding an eruption."