Scottish Power said the new price range of 300p to 325p, which puts a value on Thus of pounds 2.14bn to pounds 2.29bn, reflected the success of the book building exercise being conducted by Goldman Sachs, the global co-ordinator of the flotation.
Last week, Ian Russell, Scottish Power's finance director, said that the United States investment bank has had a highly positive response from investors, including US institutions.
Final pricing of the shares is due on Wednesday, when conditional dealings will begin. Some 49.9 per cent of Thus stock is to be sold to institutions around the world.
Thus provides telecom, data and call-centre services in addition to web access through Demon Internet, which it acquired for pounds 66m last year. Analysts estimate that Demon accounts for around one-third of the Thus float value.
Scottish Power shares closed down 9.5p at 579p even though analysts estimated that the increase in the Thus float range is worth around 20p to 25p for each share in the parent company.
In the year to March, Thus, formerly known as Scottish Telecom, earned net operating profit of pounds 11.6m on sales of pounds 166.1m.
Its major customers include Scottish and London-based companies, which buy web hosting as well as telecoms networks and other Internet services.
With Thus, Scottish Power hopes to match the success of alternative telecoms network provider Energis.
Its shares have risen around eight-fold since it was floated by National Grid Group in 1997.