Abstract: High-fanout agent workloads create a growing memory bottleneck because a single task may spawn many concurrent sandbox sessions. Yet these sandboxes are far from independent: they originate from a shared template and execute related trajectories, exposing substantial template-relative and cross-sandbox memory redundancy. Conventional memory compression is poorly matched to this setting in three fundamental dimensions: how to compress, because they fail to exploit similarity across non-identical sandbox pages; what to compress, because they control page-fault overhead through conservative page selection; and when to compress, because compression is either triggered by memory pressure or performed without awareness of agent execution phases. We present AgentZip, the first memory compression system designed specifically for AI-agent sandboxes. AgentZip introduces compression mechanisms that exploit both the template-relative and cross-sandbox redundancy. It broadens the compression scope to any page with a profitable representation and shifts overhead control from compression-time page selection to restore-time prefetching. It further aligns expensive compression with LLM waiting periods to avoid interfering with foreground tool execution. Across LLM training and inference workloads, AgentZip reduces sandbox-owned memory by up to 8.7x, compared with 2.1x for the Linux configuration. Restore prefetching and agent-execution-aware scheduling reduce the slowdown of aggressive compression from as high as 3.1x to 1.40x while retaining nearly all of its memory-saving benefit.