LLM-agent memory selection often uses retrieval rankings based on record relevance or individual influence.
Such rankings cannot identify sufficient subsets under redundant or jointly necessary evidence.
We study per-decision memory sufficiency: selecting a small subset that preserves full-memory behavior.
To separate search error from model error, we introduce JointCoreBench, a benchmark with nine interaction families, six workflow domains, natural-language decisions, and exact sufficient-set oracles, and JointCore, a relevance cost-ordered group-deletion baseline that tests blocks before individual records.
On 6,912 exact conditions, cost-ordered JointCore recovers a minimum-cost sufficient set in 100.0% of cases, reduces subset evaluations from 30.00 to 11.13 (62.9%), and achieves 87.8% active-memory savings.
Across four 12B-70B model families and 432 tasks per model, its unweighted mean is 10.28 versus 16.00 model queries and 50.6% versus 43.1% minimum-cost recovery relative to cost aware singleton deletion.
Both methods preserve full-memory behavior under the deterministic primary interface.
Tests with physical deletion, UNKNOWN masks, PENDING sentinels, counterfactual values, and alternative labels identify interface dependent behavior.
JointCore is an efficient benchmark baseline; the study does not establish deployment-ready memory compression.