Some dissatisfied people want the clocks to be changed twice a year. Others suggest keeping standard summer time all year long.
The city governments and some companies in the towns of Tartu, Voru and Tamsalu have been the first to change their office hours.
Even some parts of the emergency services are considering a time change. "Police offices in the Tallinn region may begin work 30 minutes earlier at 8 a.m. starting May 1," said Kristo Kelder, a spokesman for the Tallinn police department.
The mayor of Tamsalu, Urmas Tamm, said it would be better if institutions like banks, post offices and polyclinics worked normal hours, because it would be convenient for the people of Tamsalu to visit these places after work.
However, he added that local municipality office workers would start work earlier from May 1. It is not yet known whether this would mean an hour or a half-hour change.
"People want to live in the daylight and sleep when it gets dark," said Tamm. "We do not have daylight for long. It starts getting darker after Midsummer Day on June 24. Our employees have agreed to start earlier. The only problems are the opening times for schools and kindergartens, and bus timetables, which will not be changed."
He said he had talked to the three biggest companies in Tamsalu and all agreed to also start earlier. These companies have offices in other towns as well and they will have to coordinate their work accordingly.
Vardo Arusaar, the director of Tamsalu College, said that parents have decided to continue with the same school hours. The school year is ending in a month and a half and students will not be able to accept the new regime.
"Young people will not be going to sleep any earlier and they will be sleepy in the morning. They want to see their favorite TV shows in the evening and they might not get as much sleep as they need. Also the bus timetables will not change," said Arusaar.
Arusaar said that he would prefer having the same time all year round, because turning the clocks back and forth would be difficult for adults and children to remember. His work starts at 8 a.m., but he generally wakes up early.
"I am awake at five. I talk to my cat. But in the evenings I get tired early," said Arusaar.
In Voru county, the local governor ordered that from April 1 the employees of the local municipality should start at 7:30 a.m. and work until 4 p.m.
Raul Tohv, an assistant to the governor, said that none of the employees had protested the new hours, which enable them to spend more time on household chores.
"The sun rises at 6.30. It's much more effective to work in the mornings," he said.
The local government and enterprises of Tartu are also planning to change their working hours, from May 1. Members of the Tartu Toome Rotary Club, which includes representatives from different areas, sent a note to the mayor asking to change the opening hours of all enterprises and government institutions until the beginning of October.
Enn Seppet, head of the club's Tartu region, did not know how many enterprises had followed suit.
Sven Mikser, an assistant to the head of the opposition Center Party, said he did not like the chaotic idea of every town in Estonia working at different times.
"The government should enforce the different working hours as soon as possible. The whole of Europe turns its clocks around twice a year. I think it's wise not to get our times mixed up with our neighbors," said Mikser.
Hansapank, Estonia's largest bank, decided on April 24 not to shift its working hours because it would be difficult, representatives said, to cooperate with companies that start later.
Kristiina Tamberg, a spokeswoman for Hansapank, said that the bank had been considering earlier working hours because it would give employees more spare time after work.