diff --git a/mempool/reactor_test.go b/mempool/reactor_test.go
index 75b946a0e..400e47e84 100644
--- a/mempool/reactor_test.go
+++ b/mempool/reactor_test.go
@@ -37,7 +37,11 @@ func (ps peerState) GetHeight() int64 {
 // be received in the others.
 func TestReactorBroadcastTxMessage(t *testing.T) {
 	config := cfg.TestConfig()
-	const N = 4
+	// if there were more than two reactors, the order of transactions could not be
+	// asserted in waitForTxsOnReactors (due to transactions gossiping). If we
+	// replace Connect2Switches (full mesh) with a func, which connects first
+	// reactor to others and nothing else, this test should also pass with >2 reactors.
+	const N = 2
 	reactors := makeAndConnectReactors(config, N)
 	defer func() {
 		for _, r := range reactors {
diff --git a/types/validator_set_test.go b/types/validator_set_test.go
index 15c33930e..d17d78d1e 100644
--- a/types/validator_set_test.go
+++ b/types/validator_set_test.go
@@ -1232,21 +1232,21 @@ func TestValSetUpdatePriorityOrderTests(t *testing.T) {
 func verifyValSetUpdatePriorityOrder(t *testing.T, valSet *ValidatorSet, cfg testVSetCfg, nMaxElections int) {
 	// Run election up to nMaxElections times, sort validators by priorities
 	valSet.IncrementProposerPriority(tmrand.Int()%nMaxElections + 1)
-	origValsPriSorted := validatorListCopy(valSet.Validators)
-	sort.Sort(validatorsByPriority(origValsPriSorted))
 
 	// apply the changes, get the updated validators, sort by priorities
 	applyChangesToValSet(t, nil, valSet, cfg.addedVals, cfg.updatedVals, cfg.deletedVals)
-	updatedValsPriSorted := validatorListCopy(valSet.Validators)
-	sort.Sort(validatorsByPriority(updatedValsPriSorted))
 
 	// basic checks
 	assert.Equal(t, cfg.expectedVals, toTestValList(valSet.Validators))
 	verifyValidatorSet(t, valSet)
 
 	// verify that the added validators have the smallest priority:
-	//  - they should be at the beginning of valListNewPriority since it is sorted by priority
+	//  - they should be at the beginning of updatedValsPriSorted since it is
+	//  sorted by priority
 	if len(cfg.addedVals) > 0 {
+		updatedValsPriSorted := validatorListCopy(valSet.Validators)
+		sort.Sort(validatorsByPriority(updatedValsPriSorted))
+
 		addedValsPriSlice := updatedValsPriSorted[:len(cfg.addedVals)]
 		sort.Sort(ValidatorsByVotingPower(addedValsPriSlice))
 		assert.Equal(t, cfg.addedVals, toTestValList(addedValsPriSlice))