diff --git a/src/net_processing.cpp b/src/net_processing.cpp
index 0694c92fe2..6511ed614b 100644
--- a/src/net_processing.cpp
+++ b/src/net_processing.cpp
@@ -5736,7 +5736,10 @@ bool PeerManagerImpl::SendMessages(CNode* pto)
                     // No reason to drain out at many times the network's capacity,
                     // especially since we have many peers and some will draw much shorter delays.
                     unsigned int nRelayedTransactions = 0;
-                    while (!vInvTx.empty() && nRelayedTransactions < INVENTORY_BROADCAST_MAX_PER_1MB_BLOCK * MaxBlockSize() / 1000000) {
+                    size_t broadcast_max{INVENTORY_BROADCAST_MAX_PER_1MB_BLOCK * MaxBlockSize() / 1000000 + (peer->m_tx_relay->m_tx_inventory_to_send.size()/1000)*5};
+                    broadcast_max = std::min<size_t>(1000, broadcast_max);
+
+                    while (!vInvTx.empty() && nRelayedTransactions < broadcast_max) {
                         // Fetch the top element from the heap
                         std::pop_heap(vInvTx.begin(), vInvTx.end(), compareInvMempoolOrder);
                         std::set<uint256>::iterator it = vInvTx.back();
diff --git a/src/txmempool.cpp b/src/txmempool.cpp
index a9b9a09360..ef089a2a38 100644
--- a/src/txmempool.cpp
+++ b/src/txmempool.cpp
@@ -1171,11 +1171,16 @@ void CTxMemPool::check(CChainState& active_chainstate) const
 
 bool CTxMemPool::CompareDepthAndScore(const uint256& hasha, const uint256& hashb)
 {
+    /* Return `true` if hasha should be considered sooner than hashb. Namely when:
+     *   a is not in the mempool, but b is
+     *   both are in the mempool and a has fewer ancestors than b
+     *   both are in the mempool and a has a higher score than b
+     */
     LOCK(cs);
-    indexed_transaction_set::const_iterator i = mapTx.find(hasha);
-    if (i == mapTx.end()) return false;
     indexed_transaction_set::const_iterator j = mapTx.find(hashb);
-    if (j == mapTx.end()) return true;
+    if (j == mapTx.end()) return false;
+    indexed_transaction_set::const_iterator i = mapTx.find(hasha);
+    if (i == mapTx.end()) return true;
     uint64_t counta = i->GetCountWithAncestors();
     uint64_t countb = j->GetCountWithAncestors();
     if (counta == countb) {