diff --git a/src/Expr.cc b/src/Expr.cc
index dde0575490..b073db85b6 100644
--- a/src/Expr.cc
+++ b/src/Expr.cc
@@ -1390,6 +1390,36 @@ void AddExpr::Canonicalize() {
         SwapOps();
 }
 
+// True if we should treat LHS += RHS as add-every-element-of-RHS-to-LHS.
+// False for the alternative, add-RHS-as-one-element-to-LHS.
+//
+// Assumes (1) LHS has already been confirmed as a vector, (2) the
+// "LHS += RHS" expression has been type-checked.
+
+static bool is_element_wise_vector_append(const TypePtr& lhs, const TypePtr& rhs) {
+    if ( ! IsVector(rhs->Tag()) )
+        // Can't be add-every-element since RHS isn't even a vector.
+        return false;
+
+    if ( ! same_type(lhs, rhs) )
+        // Can't be add-every-element since they're different types of vectors.
+        return false;
+
+    if ( lhs->Yield()->Tag() != TYPE_VECTOR )
+        // LHS is not a vector-of-vector, and RHS is a vector, so
+        // clearly we're doing element-wise-append.
+        return true;
+
+    if ( rhs->AsVectorType()->IsUnspecifiedVector() )
+        // This is a vector-of-vector-of-X += vector() construct.
+        // It is *not* treated as element-wise-append of an empty RHS,
+        // instead append an empty vector to the LHS.
+        return false;
+
+    // RHS is a compatible element-wise-append vector for LHS.
+    return true;
+}
+
 AddToExpr::AddToExpr(ExprPtr arg_op1, ExprPtr arg_op2)
     : BinaryExpr(EXPR_ADD_TO, std::move(arg_op1), std::move(arg_op2)) {
     if ( IsError() )
@@ -1426,9 +1456,9 @@ AddToExpr::AddToExpr(ExprPtr arg_op1, ExprPtr arg_op2)
     }
 
     else if ( IsVector(bt1) ) {
-        // We need the IsVector(bt2) check in the following because
-        // same_type() always treats "any" types as "same".
-        if ( IsVector(bt2) && same_type(t1, t2) ) {
+        // Treat += of two vectors as appending each element
+        // of the RHS to the LHS if types agree.
+        if ( is_element_wise_vector_append(t1, t2) ) {
             SetType(t1);
             return;
         }
diff --git a/src/Expr.h b/src/Expr.h
index bc0990fcec..fc22549ca3 100644
--- a/src/Expr.h
+++ b/src/Expr.h
@@ -713,6 +713,8 @@ public:
     AddToExpr(ExprPtr op1, ExprPtr op2);
     ValPtr Eval(Frame* f) const override;
 
+    bool IsVectorElemAppend() const { return is_vector_elem_append; }
+
     // Optimization-related:
     bool IsPure() const override { return false; }
     ExprPtr Duplicate() override;
diff --git a/src/script_opt/CPP/Exprs.cc b/src/script_opt/CPP/Exprs.cc
index ed0591ed51..9cdcba0a44 100644
--- a/src/script_opt/CPP/Exprs.cc
+++ b/src/script_opt/CPP/Exprs.cc
@@ -481,10 +481,10 @@ string CPPCompile::GenAddToExpr(const Expr* e, GenType gt, bool top_level) {
     if ( t->Tag() == TYPE_VECTOR ) {
         auto& rt = rhs->GetType();
 
-        if ( IsVector(rt->Tag()) && same_type(lhs->GetType(), rt) )
-            add_to_func = "vector_vec_append__CPP";
-        else
+        if ( e->AsAddToExpr()->IsVectorElemAppend() )
             add_to_func = "vector_append__CPP";
+        else
+            add_to_func = "vector_vec_append__CPP";
     }
 
     else if ( t->Tag() == TYPE_PATTERN )
diff --git a/src/script_opt/Expr.cc b/src/script_opt/Expr.cc
index fe6e789dc2..235a5f09f0 100644
--- a/src/script_opt/Expr.cc
+++ b/src/script_opt/Expr.cc
@@ -764,7 +764,7 @@ ExprPtr AddToExpr::Reduce(Reducer* c, StmtPtr& red_stmt) {
 
             red_stmt = MergeStmts(red_stmt1, red_stmt2);
 
-            if ( tag == TYPE_VECTOR && (! IsVector(op2->GetType()->Tag()) || ! same_type(t, op2->GetType())) ) {
+            if ( is_vector_elem_append ) {
                 auto append = with_location_of(make_intrusive<AppendToExpr>(op1->Duplicate(), op2), this);
                 auto append_stmt = with_location_of(make_intrusive<ExprStmt>(append), this);
 
diff --git a/testing/btest/Baseline/language.vector/out b/testing/btest/Baseline/language.vector/out
index a4f4bce8d3..5887d66595 100644
--- a/testing/btest/Baseline/language.vector/out
+++ b/testing/btest/Baseline/language.vector/out
@@ -82,3 +82,5 @@ left shift (PASS)
 right shift (PASS)
 negative index (PASS)
 negative index (PASS)
++= of empty vector (PASS)
++= of empty vector (PASS)
diff --git a/testing/btest/language/vector.zeek b/testing/btest/language/vector.zeek
index d8bb810181..820261e0e8 100644
--- a/testing/btest/language/vector.zeek
+++ b/testing/btest/language/vector.zeek
@@ -229,4 +229,16 @@ event zeek_init()
 	test_case( "negative index", v24[-1] == 5 );
 	test_case( "negative index", v24[-3] == 3 );
 
+	# For a vector-of-vectors, += of an empty vector should append it as
+	# a single element, not all of its elements (= nothing gets appended).
+	local v25: vector of vector of count;
+	v25 += vector();
+	test_case( "+= of empty vector", |v25| == 1 );
+
+	# OTOH, for a vector-of-non-vectors, it should result in appending
+	# nothing.
+	local v26: vector of set[count];
+	v26 += vector();
+	test_case( "+= of empty vector", |v26| == 0 );
+
 }