diff --git a/sweep/fee_function.go b/sweep/fee_function.go
index db3fb7851..955ca43a6 100644
--- a/sweep/fee_function.go
+++ b/sweep/fee_function.go
@@ -6,6 +6,7 @@ import (
 
 	"github.com/btcsuite/btcd/btcutil"
 	"github.com/lightningnetwork/lnd/lnwallet/chainfee"
+	"github.com/lightningnetwork/lnd/lnwire"
 )
 
 var (
@@ -14,6 +15,17 @@ var (
 	ErrMaxPosition = errors.New("position already at max")
 )
 
+// mSatPerKWeight represents a fee rate in msat/kw.
+//
+// TODO(yy): unify all the units to be virtual bytes.
+type mSatPerKWeight lnwire.MilliSatoshi
+
+// String returns a human-readable string of the fee rate.
+func (m mSatPerKWeight) String() string {
+	s := lnwire.MilliSatoshi(m)
+	return fmt.Sprintf("%v/kw", s)
+}
+
 // FeeFunction defines an interface that is used to calculate fee rates for
 // transactions. It's expected the implementations use three params, the
 // starting fee rate, the ending fee rate, and number of blocks till deadline
@@ -80,8 +92,10 @@ type LinearFeeFunction struct {
 	// and the current block height.
 	position uint32
 
-	// deltaFeeRate is the fee rate increase per block.
-	deltaFeeRate chainfee.SatPerKWeight
+	// deltaFeeRate is the fee rate (msat/kw) increase per block.
+	//
+	// NOTE: this is used to increase precision.
+	deltaFeeRate mSatPerKWeight
 
 	// estimator is the fee estimator used to estimate the fee rate. We use
 	// it to get the initial fee rate and, use it as a benchmark to decide
@@ -121,21 +135,28 @@ func NewLinearFeeFunction(maxFeeRate chainfee.SatPerKWeight, confTarget uint32,
 
 	// Calculate how much fee rate should be increased per block.
 	end := l.endingFeeRate
-	delta := btcutil.Amount(end - start).MulF64(1 / float64(confTarget))
+
+	// The starting and ending fee rates are in sat/kw, so we need to
+	// convert them to msat/kw by multiplying by 1000.
+	delta := btcutil.Amount(end - start).MulF64(1000 / float64(confTarget))
+	l.deltaFeeRate = mSatPerKWeight(delta)
 
 	// We only allow the delta to be zero if the width is one - when the
 	// delta is zero, it means the starting and ending fee rates are the
 	// same, which means there's nothing to increase, so any width greater
 	// than 1 doesn't provide any utility. This could happen when the
 	// sweeper is offered to sweep an input that has passed its deadline.
-	if delta == 0 && l.width != 1 {
+	if l.deltaFeeRate == 0 && l.width != 1 {
+		log.Errorf("Failed to init fee function: startingFeeRate=%v, "+
+			"endingFeeRate=%v, width=%v, delta=%v", start, end,
+			confTarget, l.deltaFeeRate)
+
 		return nil, fmt.Errorf("fee rate delta is zero")
 	}
 
 	// Attach the calculated values to the fee function.
 	l.startingFeeRate = start
 	l.currentFeeRate = start
-	l.deltaFeeRate = chainfee.SatPerKWeight(delta)
 
 	log.Debugf("Linear fee function initialized with startingFeeRate=%v, "+
 		"endingFeeRate=%v, width=%v, delta=%v", start, end,
@@ -234,7 +255,9 @@ func (l *LinearFeeFunction) feeRateAtPosition(p uint32) chainfee.SatPerKWeight {
 		return l.endingFeeRate
 	}
 
-	feeRateDelta := btcutil.Amount(l.deltaFeeRate).MulF64(float64(p))
+	// deltaFeeRate is in msat/kw, so we need to divide by 1000 to get the
+	// fee rate in sat/kw.
+	feeRateDelta := btcutil.Amount(l.deltaFeeRate).MulF64(float64(p) / 1000)
 
 	feeRate := l.startingFeeRate + chainfee.SatPerKWeight(feeRateDelta)
 	if feeRate > l.endingFeeRate {
diff --git a/sweep/fee_function_test.go b/sweep/fee_function_test.go
index e7f80819a..e549d8d64 100644
--- a/sweep/fee_function_test.go
+++ b/sweep/fee_function_test.go
@@ -54,8 +54,8 @@ func TestLinearFeeFunctionNew(t *testing.T) {
 	//
 	// Mock the fee estimator to return the fee rate.
 	estimator.On("EstimateFeePerKW", confTarget).Return(
-		// The starting fee rate is 1 sat/kw less than the max fee rate.
-		maxFeeRate-1, nil).Once()
+		// The starting fee rate is the max fee rate.
+		maxFeeRate, nil).Once()
 	estimator.On("RelayFeePerKW").Return(estimatedFeeRate).Once()
 
 	f, err = NewLinearFeeFunction(maxFeeRate, confTarget, estimator)
@@ -96,7 +96,7 @@ func TestLinearFeeFunctionFeeRateAtPosition(t *testing.T) {
 		startingFeeRate: 1000,
 		endingFeeRate:   3000,
 		position:        0,
-		deltaFeeRate:    1000,
+		deltaFeeRate:    1_000_000,
 		width:           3,
 	}