diff --git a/src/compile.c b/src/compile.c
index f0be1a5f..5e64946b 100644
--- a/src/compile.c
+++ b/src/compile.c
@@ -1241,6 +1241,13 @@ static int compile(struct bytecode* bc, block b, struct locfile* lf, jv args, jv
 
     if (curr->op == CLOSURE_CREATE) {
       assert(curr->bound_by == curr);
+      // Prevent subfunction index from overflowing into ARG_NEWCLOSURE flag
+      if (bc->nsubfunctions >= ARG_NEWCLOSURE) {
+        locfile_locate(lf, curr->source,
+            "too many function parameters or local function definitions (max %d)", ARG_NEWCLOSURE - 1);
+        errors++;
+        break;
+      }
       curr->imm.intval = bc->nsubfunctions++;
     }
     if (curr->op == CLOSURE_CREATE_C) {
@@ -1274,6 +1281,13 @@ static int compile(struct bytecode* bc, block b, struct locfile* lf, jv args, jv
         for (inst* param = curr->arglist.first; param; param = param->next) {
           assert(param->op == CLOSURE_PARAM);
           assert(param->bound_by == param);
+          // Prevent closure index from overflowing into ARG_NEWCLOSURE flag
+          if (subfn->nclosures >= ARG_NEWCLOSURE) {
+            locfile_locate(lf, curr->source,
+                "function has too many parameters (max %d)", ARG_NEWCLOSURE - 1);
+            errors++;
+            break;
+          }
           param->imm.intval = subfn->nclosures++;
           param->compiled = subfn;
           params = jv_array_append(params, jv_string(param->symbol));
diff --git a/tests/shtest b/tests/shtest
index e241d4a5..90a96eaf 100755
--- a/tests/shtest
+++ b/tests/shtest
@@ -844,4 +844,31 @@ if ! $msys && ! $mingw; then
   fi
 fi
 
+# Test ARG_NEWCLOSURE overflow protection (issue #3458)
+# Test 1: Too many function parameters (4097 params triggers the limit)
+echo "Testing function parameter limit..."
+cat > $d/expected <<EOF
+jq: error: too many function parameters or local function definitions (max 4095)
+jq: 1 compile error
+EOF
+$JQ -rn '"def f(\([range(4097) | "a\(.)"] | join(";"))): .; f(\([range(4097)] | join(";")))"' > $d/prog.jq
+$JQ -nf $d/prog.jq 2> $d/out && {
+  echo "Expected compile error for too many parameters"
+  exit 1
+}
+diff $d/out $d/expected
+
+# Test 2: Too many local functions (4097 functions triggers the limit)
+echo "Testing local function limit..."
+cat > $d/expected <<EOF
+jq: error: too many function parameters or local function definitions (max 4095)
+jq: 1 compile error
+EOF
+$JQ -rn '"\([range(4097) | "def f\(.): \(.)"] | join("; ")); \([range(4097) | "f\(.)"] | join(" + "))"' > $d/prog.jq
+$JQ -nf $d/prog.jq 2> $d/out && {
+  echo "Expected compile error for too many local functions"
+  exit 1
+}
+diff $d/out $d/expected
+
 exit 0