The phrase "careful deliberation" means thinking very carefully and making decisions after considering all the important information and possible outcomes. Full definition
There are many great physicist that do not agree with Hawkins assessment of God's existence and his studies have taken him further to not only deny the existence of God but to further conclude that God's dwelling place is also non existent, after careful deliberations of course. (religion.blogs.cnn.com)
Jury's motivation: The jury decided to use their privilege to award a special mention, after a day of careful deliberation in this year's Nordic Game Awards. (conf.nordicgame.com)
Deciding between these two options requires careful deliberation. (autogen.co.za)