diff --git a/.changeset/law-credit-label.md b/.changeset/law-credit-label.md
new file mode 100644
index 0000000..e330623
--- /dev/null
+++ b/.changeset/law-credit-label.md
@@ -0,0 +1,5 @@
+---
+'@tanstack/oracles': patch
+---
+
+The gap report's per-law table is now titled "First law to reject, by law". It says that each count credits only the first law that rejected a history, because a check returns its first violation and a later law on the same history is not checked. A law with no count is not shown to reject nothing. The section's next step tells the author to add a history that varies the input the law judges.
diff --git a/packages/oracles/oracle-gaps/gap-report-classify-oracle.property.test.mjs b/packages/oracles/oracle-gaps/gap-report-classify-oracle.property.test.mjs
index 821f915..80976b1 100644
--- a/packages/oracles/oracle-gaps/gap-report-classify-oracle.property.test.mjs
+++ b/packages/oracles/oracle-gaps/gap-report-classify-oracle.property.test.mjs
@@ -883,7 +883,7 @@ function model(h) {
 // sentence after its directive.
 const boundaryLine = `Add a boundary history with -0 and 0.`
 // The kills-by-law section's one next step for a law that rejects no mutant.
-const killsDirective = `To find a law that rejects no mutant, add a history that varies the input the law judges, and run the check again.`
+const killsDirective = `Each count credits only the first law that rejected a history: a later law on the same history is not checked. To test a law with no count, add a history that varies the input the law judges, and run the check again.`
 const exits =
   /equivalen|maintainer|approv|allowance|either|whether|\bor\b|\bif no\b|limit|accept|\?|\bsay\b/i
 const directives = {
@@ -1295,7 +1295,9 @@ async function driver(h, observe) {
     streamed: printer
       ? [...report.gapsOf(results)].reverse().map((r) => printer.gapLine(r))
       : undefined,
-    killsSection: summary.slice(summary.indexOf(`## Kills by law`)),
+    killsSection: summary.slice(
+      summary.indexOf(`## First law to reject, by law`),
+    ),
     // What results.json keeps of each mutant's change, after the printing.
     kept: results.map((r) =>
       r.authored ? r.intent : [String(r.original), String(r.replacement)],
diff --git a/packages/oracles/oracle-gaps/report.mjs b/packages/oracles/oracle-gaps/report.mjs
index 6b023bf..d83b75b 100644
--- a/packages/oracles/oracle-gaps/report.mjs
+++ b/packages/oracles/oracle-gaps/report.mjs
@@ -172,7 +172,10 @@ const placeholders = {
 const legendOf = (kind) => directive[kind]({ ...placeholders, outcome: kind })
 
 // What the author does about a law that rejects no mutant: one next step.
-const killsDirective = `To find a law that rejects no mutant, add a history that varies the input the law judges, and run the check again.`
+// The table credits each history's first rejecting law only: a check returns
+// its first violation, so a later law on the same history is never judged.
+// The count says which law rejected first, not which laws can reject.
+const killsDirective = `Each count credits only the first law that rejected a history: a later law on the same history is not checked. To test a law with no count, add a history that varies the input the law judges, and run the check again.`
 
 export function gapsOf(results) {
   return results.filter(
@@ -290,11 +293,11 @@ export function renderReport({ results, run, excluded }) {
     for (const law of result.laws ?? [])
       byLaw.set(law, (byLaw.get(law) ?? 0) + 1)
   lines.push(
-    `## Kills by law`,
+    `## First law to reject, by law`,
     ``,
     killsDirective,
     ``,
-    `| Law | Mutants it rejected |`,
+    `| Law | Mutants it rejected first |`,
     `|---|---|`,
     ...[...byLaw]
       .sort((a, b) => b[1] - a[1])