While in clear-cut situations automated analytical solution for data streams are already in place, only few visual approaches have been proposed in the literature for exploratory analysis tasks on dynamic information. However, due to the competitive or security-related advantages that real-time information gives in domains such as finance, business or networking, we are convinced that there is a need for exploratory visualization tools for data streams. Under the conditions that new events have higher relevance and that smooth transitions enable traceability of items, we propose a novel dynamic stream visualization called StreamSqueeze. In this technique the degree of interest of recent items is expressed through an increase in size and thus recent events can be shown with more details. The technique has two main benefits: First, the layout algorithm arranges items in several lists of various sizes and optimizes the positions within each list so that the transition of an item from one list to the other triggers least visual changes. Second, the animation scheme ensures that for 50 percent of the time an item has a static screen position where reading is most effective and then continuously shrinks and moves to the its next static position in the subsequent list. To demonstrate the capability of our technique, we apply it to large and high-frequency news and syslog streams and show how it maintains optimal stability of the layout under the conditions given above.