While the law will contain a ban on bypassing copy protection on CDs, and DVDs , Parliament will add a note to the preamble of the law stating the right of consumers to copy digital media for private use.
Problems have been caused by a section of the bill, which would make it illegal to make a copy of a copy-protected CD or DVD for personal use.
Up to now, consumers have been able to copy any digital media which they have legally purchased. Copying music, movies and even backing up commercial software has been allowed.
News of a change in the law brought a flood of protesting email - much of it from young people who fear that the bill could effectively make it illegal to copy CDs onto MP3 players.
Copyright holders' groups have pushed to have the law passed "as is", arguing it is the only way to prevent the spread of pirate copies over the Internet.
On Wednesday, the parliamentary groups of the government parties and Minister of Culture Tanja Karpela agreed that a separate clause will be inserted in the preamble of the bill saying that the recording industry should act to ensure that consumers will continue to have the possibility to make a few copies of copyright materials for private use.
Critics of the bill have claimed that the legislation will not only hurt consumers, but that it also encourages a more general disregard for the law. While breaking of copy protection for the copying of the content of a sound or video recording for personal use would be prohibited, it will carry no specific criminal penalty. They say the law will not only be unenforcable - it may also teach the young that not all laws have to be observed.
Some legal experts think that Parliament is ducking responsibility and hoping that the courts will eventually sort out copyright law.