diff --git a/src/AddImageChecks.cpp b/src/AddImageChecks.cpp
index e9ca8ae25be9..72f2596fe12b 100644
--- a/src/AddImageChecks.cpp
+++ b/src/AddImageChecks.cpp
@@ -106,11 +106,21 @@ class TrimStmtToPartsThatAccessBuffers : public IRMutator {
     using IRMutator::visit;
 
     Expr visit(const Call *op) override {
-        touches_buffer |= (buffers.count(op->name) > 0);
+        touches_buffer |=
+            (buffers.count(op->name) > 0) ||
+            (buffers.count(op->name + "." + std::to_string(op->value_index)));
+        // Output Tuple params are in the buffers map under their qualified
+        // tuple name, not the Func name.
         return IRMutator::visit(op);
     }
     Stmt visit(const Provide *op) override {
-        touches_buffer |= (buffers.find(op->name) != buffers.end());
+        if (op->values.size() == 1) {
+            touches_buffer |= (buffers.find(op->name) != buffers.end());
+        } else {
+            // It's a Tuple. Just check if the first Tuple component corresponds
+            // to an output buffer. If it does, they all do.
+            touches_buffer |= (buffers.find(op->name + ".0") != buffers.end());
+        }
         return IRMutator::visit(op);
     }
     Expr visit(const Variable *op) override {
diff --git a/test/error/CMakeLists.txt b/test/error/CMakeLists.txt
index ee9d47923469..f85ede60d7a8 100644
--- a/test/error/CMakeLists.txt
+++ b/test/error/CMakeLists.txt
@@ -94,6 +94,7 @@ tests(GROUPS error
       thread_id_outside_block_id.cpp
       too_many_args.cpp
       tuple_arg_select_undef.cpp
+      tuple_output_bounds_check.cpp
       tuple_val_select_undef.cpp
       unbounded_input.cpp
       unbounded_output.cpp
diff --git a/test/error/tuple_output_bounds_check.cpp b/test/error/tuple_output_bounds_check.cpp
new file mode 100644
index 000000000000..53b3a26a8337
--- /dev/null
+++ b/test/error/tuple_output_bounds_check.cpp
@@ -0,0 +1,26 @@
+#include "Halide.h"
+
+using namespace Halide;
+
+int main(int argc, char **argv) {
+    // The code below used to not inject appropriate bounds checks.
+    // See https://github.com/halide/Halide/issues/7343
+
+    Var x;
+
+    const int size = 1024;
+
+    Func h;
+    h(x) = {0, 0};
+    RDom r(0, size);
+    h(r) = {h(r - 100)[0], 0};
+
+    Var xo, xi;
+    h.split(x, xo, xi, 16, TailStrategy::RoundUp);
+
+    Buffer<int> r0(size);
+    Buffer<int> r1(size);
+    h.realize({r0, r1});
+
+    return 0;
+}