diff --git a/src/parser3.h b/src/parser3.h
index 639a05f..fba123c 100644
--- a/src/parser3.h
+++ b/src/parser3.h
@@ -139,7 +139,7 @@ struct Parser3 {
     stackPtr = stack();
     std::ignore = push({N_VALUE, N_WHITESPACE, T_EOF});
     inKey = false;
-    rejected = false;
+    terminalStatus = WeaselJson_OK;
     utf8Codepoint = 0;
     utf16Surrogate = 0;
     minCodepoint = 0;
@@ -162,7 +162,7 @@ struct Parser3 {
   NumDfa numDfa;
   Utf8Dfa strDfa;
   bool inKey = false;
-  bool rejected = false;
+  WeaselJsonStatus terminalStatus = WeaselJson_OK;
 
 #ifndef HAS_MUSTTAIL
   char *stashBufForTrampoline;
@@ -1070,12 +1070,12 @@ constexpr inline struct ContinuationTable {
 inline WeaselJsonStatus Parser3::parse(char *buf, int len) {
   this->dataBegin = this->writeBuf = buf;
 
-  if (this->rejected) [[unlikely]] {
-    return WeaselJson_REJECT;
+  if (this->terminalStatus != WeaselJson_OK) [[unlikely]] {
+    return this->terminalStatus;
   }
 
   if (len < 0) [[unlikely]] {
-    this->rejected = true;
+    this->terminalStatus = WeaselJson_REJECT;
     return WeaselJson_REJECT;
   }
 
@@ -1085,8 +1085,8 @@ inline WeaselJsonStatus Parser3::parse(char *buf, int len) {
   // range.
   ContinuationStatus status =
       symbolTables.continuations[top()](this, buf, buf + len);
-  if (status == WeaselJson_REJECT) {
-    this->rejected = true;
+  if (status > WeaselJson_AGAIN) {
+    this->terminalStatus = WeaselJsonStatus(status);
   }
   return WeaselJsonStatus(status);
 #else
@@ -1095,8 +1095,8 @@ inline WeaselJsonStatus Parser3::parse(char *buf, int len) {
   while ((result = symbolTables.continuations[top()](
               this, stashBufForTrampoline, buf + len)) == kBounce)
     ;
-  if (result == WeaselJson_REJECT) {
-    this->rejected = true;
+  if (result > WeaselJson_AGAIN) {
+    this->terminalStatus = WeaselJsonStatus(result);
   }
   return WeaselJsonStatus(result);
 #endif
diff --git a/src/test.cpp b/src/test.cpp
index d13d353..6fef3a7 100644
--- a/src/test.cpp
+++ b/src/test.cpp
@@ -202,6 +202,62 @@ TEST_CASE("parser3") {
   }
 }
 
+TEST_CASE("overflow state is sticky") {
+  auto c = noopCallbacks();
+  // stackSize 3 is exactly big enough to hold reset()'s bootstrap, but too
+  // small for nested arrays. Overflows must be terminal like rejects: a later
+  // end-of-data call must never report OK for an incomplete document.
+  auto *parser = WeaselJsonParser_create(3, &c, nullptr, 0);
+  REQUIRE(parser != nullptr);
+
+  std::string doc = "[[";
+  REQUIRE(WeaselJsonParser_parse(parser, doc.data(), doc.size()) ==
+          WeaselJson_OVERFLOW);
+
+  // After overflow, the end-of-data call must not return OK.
+  REQUIRE(WeaselJsonParser_parse(parser, nullptr, 0) != WeaselJson_OK);
+  // It should keep reporting a terminal failure.
+  REQUIRE(WeaselJsonParser_parse(parser, nullptr, 0) != WeaselJson_OK);
+
+  // Further data chunks must also stay terminal.
+  std::string more = "]]";
+  REQUIRE(WeaselJsonParser_parse(parser, more.data(), more.size()) !=
+          WeaselJson_OK);
+
+  WeaselJsonParser_destroy(parser);
+}
+
+TEST_CASE("overflow is sticky for nested objects") {
+  auto c = noopCallbacks();
+  auto *parser = WeaselJsonParser_create(4, &c, nullptr, 0);
+  REQUIRE(parser != nullptr);
+
+  std::string doc = "{\"a\":{ \"a\":";
+  REQUIRE(WeaselJsonParser_parse(parser, doc.data(), doc.size()) ==
+          WeaselJson_OVERFLOW);
+  REQUIRE(WeaselJsonParser_parse(parser, nullptr, 0) != WeaselJson_OK);
+
+  WeaselJsonParser_destroy(parser);
+}
+
+TEST_CASE("reset clears overflow state") {
+  auto c = noopCallbacks();
+  auto *parser = WeaselJsonParser_create(3, &c, nullptr, 0);
+  REQUIRE(parser != nullptr);
+
+  std::string doc = "[[";
+  REQUIRE(WeaselJsonParser_parse(parser, doc.data(), doc.size()) ==
+          WeaselJson_OVERFLOW);
+  // After reset the parser should accept a minimal document again.
+  WeaselJsonParser_reset(parser);
+  std::string copy = "1";
+  REQUIRE(WeaselJsonParser_parse(parser, copy.data(), copy.size()) ==
+          WeaselJson_AGAIN);
+  REQUIRE(WeaselJsonParser_parse(parser, nullptr, 0) == WeaselJson_OK);
+
+  WeaselJsonParser_destroy(parser);
+}
+
 TEST_CASE("rejected state is sticky") {
   auto c = noopCallbacks();
   auto *parser = WeaselJsonParser_create(1024, &c, nullptr, 0);