diff --git a/src/net_processing.cpp b/src/net_processing.cpp
--- a/src/net_processing.cpp
+++ b/src/net_processing.cpp
@@ -3086,8 +3086,8 @@
                              txid.ToString(), pfrom.GetId());
                     pfrom.fDisconnect = true;
                     return;
-                } else if (!fAlreadyHave && !fImporting && !fReindex &&
-                           !::ChainstateActive().IsInitialBlockDownload()) {
+                } else if (!fAlreadyHave && !m_chainman.ActiveChainstate()
+                                                 .IsInitialBlockDownload()) {
                     RequestTx(State(pfrom.GetId()), txid, current_time);
                 }
             }
@@ -5524,11 +5524,23 @@
                         1000000)
                     .GetFeePerK();
             int64_t timeNow = GetTimeMicros();
+            static FeeFilterRounder g_filter_rounder{
+                CFeeRate{DEFAULT_MIN_RELAY_TX_FEE_PER_KB}};
+            if (m_chainman.ActiveChainstate().IsInitialBlockDownload()) {
+                // Received tx-inv messages are discarded when the active
+                // chainstate is in IBD, so tell the peer to not send them.
+                currentFilter = MAX_MONEY;
+            } else {
+                static const Amount MAX_FILTER{
+                    g_filter_rounder.round(MAX_MONEY)};
+                if (pto->m_tx_relay->lastSentFeeFilter == MAX_FILTER) {
+                    // Send the current filter if we sent MAX_FILTER previously
+                    // and made it out of IBD.
+                    pto->m_tx_relay->nextSendTimeFeeFilter = timeNow - 1;
+                }
+            }
             if (timeNow > pto->m_tx_relay->nextSendTimeFeeFilter) {
-                static CFeeRate default_feerate =
-                    CFeeRate(DEFAULT_MIN_RELAY_TX_FEE_PER_KB);
-                static FeeFilterRounder filterRounder(default_feerate);
-                Amount filterToSend = filterRounder.round(currentFilter);
+                Amount filterToSend = g_filter_rounder.round(currentFilter);
                 filterToSend =
                     std::max(filterToSend, ::minRelayTxFee.GetFeePerK());
 
diff --git a/src/test/CMakeLists.txt b/src/test/CMakeLists.txt
--- a/src/test/CMakeLists.txt
+++ b/src/test/CMakeLists.txt
@@ -175,6 +175,7 @@
 		netbase_tests.cpp
 		op_reversebytes_tests.cpp
 		pmt_tests.cpp
+		policy_fee_tests.cpp
 		policyestimator_tests.cpp
 		prevector_tests.cpp
 		radix_tests.cpp
diff --git a/src/test/policy_fee_tests.cpp b/src/test/policy_fee_tests.cpp
new file mode 100644
--- /dev/null
+++ b/src/test/policy_fee_tests.cpp
@@ -0,0 +1,34 @@
+// Copyright (c) 2020 The Bitcoin Core developers
+// Distributed under the MIT software license, see the accompanying
+// file COPYING or http://www.opensource.org/licenses/mit-license.php.
+
+#include <amount.h>
+#include <feerate.h>
+#include <policy/fees.h>
+
+#include <test/util/setup_common.h>
+
+#include <boost/test/unit_test.hpp>
+
+BOOST_FIXTURE_TEST_SUITE(policy_fee_tests, BasicTestingSetup)
+
+BOOST_AUTO_TEST_CASE(FeeRounder) {
+    FeeFilterRounder fee_rounder{CFeeRate{1000 * SATOSHI}};
+
+    // check that 1000 rounds to 974 or 1071
+    std::set<Amount> results;
+    while (results.size() < 2) {
+        results.emplace(fee_rounder.round(1000 * SATOSHI));
+    }
+    BOOST_CHECK_EQUAL(*results.begin(), 974 * SATOSHI);
+    BOOST_CHECK_EQUAL(*++results.begin(), 1071 * SATOSHI);
+
+    // check that negative amounts rounds to 0
+    BOOST_CHECK_EQUAL(fee_rounder.round(-0 * SATOSHI), Amount::zero());
+    BOOST_CHECK_EQUAL(fee_rounder.round(-1 * SATOSHI), Amount::zero());
+
+    // check that MAX_MONEY rounds to 9170997
+    BOOST_CHECK_EQUAL(fee_rounder.round(MAX_MONEY), 9170997 * SATOSHI);
+}
+
+BOOST_AUTO_TEST_SUITE_END()
diff --git a/src/validation.h b/src/validation.h
--- a/src/validation.h
+++ b/src/validation.h
@@ -1115,7 +1115,8 @@
     std::vector<CChainState *> GetAll();
 
     //! The most-work chain.
-    CChain &ActiveChain() const;
+    CChainState &ActiveChainstate() const;
+    CChain &ActiveChain() const { return ActiveChainstate().m_chain; }
     int ActiveHeight() const { return ActiveChain().Height(); }
     CBlockIndex *ActiveTip() const { return ActiveChain().Tip(); }
 
@@ -1217,13 +1218,13 @@
  */
 extern ChainstateManager g_chainman GUARDED_BY(::cs_main);
 
-/** @returns the most-work valid chainstate. */
+/** Please prefer the identical ChainstateManager::ActiveChainstate */
 CChainState &ChainstateActive();
 
-/** @returns the most-work chain. */
+/** Please prefer the identical ChainstateManager::ActiveChain */
 CChain &ChainActive();
 
-/** @returns the global block index map. */
+/** Please prefer the identical ChainstateManager::BlockIndex */
 BlockMap &BlockIndex();
 
 /**
diff --git a/src/validation.cpp b/src/validation.cpp
--- a/src/validation.cpp
+++ b/src/validation.cpp
@@ -6092,9 +6092,9 @@
     return *to_modify;
 }
 
-CChain &ChainstateManager::ActiveChain() const {
+CChainState &ChainstateManager::ActiveChainstate() const {
     assert(m_active_chainstate);
-    return m_active_chainstate->m_chain;
+    return *m_active_chainstate;
 }
 
 bool ChainstateManager::IsSnapshotActive() const {
diff --git a/test/functional/rpc_net.py b/test/functional/rpc_net.py
--- a/test/functional/rpc_net.py
+++ b/test/functional/rpc_net.py
@@ -51,6 +51,8 @@
         self.supports_cli = False
 
     def run_test(self):
+        self.log.info('Get out of IBD for the minfeefilter test')
+        self.nodes[0].generate(1)
         self.log.info('Connect nodes both way')
         connect_nodes(self.nodes[0], self.nodes[1])
         connect_nodes(self.nodes[1], self.nodes[0])