diff --git a/fragment.go b/fragment.go
index c6cc03291..728fe9dee 100644
--- a/fragment.go
+++ b/fragment.go
@@ -118,8 +118,6 @@ type fragment struct {
 
 	// Stats reporting.
 	maxRowID uint64
-	minRowID uint64
-	hasRowID bool
 
 	// Cache containing full rows (not just counts).
 	rowCache bitmapCache
@@ -191,9 +189,6 @@ func (f *fragment) Open() error {
 
 		// Read last bit to determine max row.
 		f.maxRowID = f.storage.Max() / ShardWidth
-		min, ok := f.storage.Min()
-		f.minRowID = min / ShardWidth
-		f.hasRowID = ok
 		f.stats.Gauge("rows", float64(f.maxRowID), 1.0)
 		return nil
 	}(); err != nil {
@@ -525,10 +520,6 @@ func (f *fragment) unprotectedSetBit(rowID, columnID uint64) (changed bool, err
 		f.maxRowID = rowID
 		f.stats.Gauge("rows", float64(f.maxRowID), 1.0)
 	}
-	if !f.hasRowID || rowID < f.minRowID {
-		f.minRowID = rowID
-		f.hasRowID = true
-	}
 
 	return changed, nil
 }
@@ -1040,12 +1031,13 @@ func (f *fragment) maxUnsigned(filter *Row, bitDepth uint) (max int64, count uin
 // if filter is nil, it returns fragment.minRowID, 1
 // if fragment has no rows, it returns 0, 0
 func (f *fragment) minRow(filter *Row) (uint64, uint64) {
-	if f.hasRowID {
+	minRowID, hasRowID := f.minRowID()
+	if hasRowID {
 		if filter == nil {
-			return f.minRowID, 1
+			return minRowID, 1
 		}
 		// iterate from min row ID and return the first that intersects with filter.
-		for i := f.minRowID; i <= f.maxRowID; i++ {
+		for i := minRowID; i <= f.maxRowID; i++ {
 			row := f.row(i).Intersect(filter)
 			count := row.Count()
 			if count > 0 {
@@ -1060,12 +1052,14 @@ func (f *fragment) minRow(filter *Row) (uint64, uint64) {
 // if filter is nil, it returns fragment.maxRowID, 1
 // if fragment has no rows, it returns 0, 0
 func (f *fragment) maxRow(filter *Row) (uint64, uint64) {
-	if f.hasRowID {
+	minRowID, hasRowID := f.minRowID()
+	if hasRowID {
 		if filter == nil {
 			return f.maxRowID, 1
 		}
 		// iterate back from max row ID and return the first that intersects with filter.
-		for i := f.maxRowID; i >= f.minRowID; i-- {
+		// TODO: implement reverse container iteration to improve performance here for sparse data. --Jaffee
+		for i := f.maxRowID; i >= minRowID; i-- {
 			row := f.row(i).Intersect(filter)
 			count := row.Count()
 			if count > 0 {
@@ -2419,6 +2413,11 @@ func (f *fragment) readCacheFromArchive(r io.Reader) error {
 	return nil
 }
 
+func (f *fragment) minRowID() (uint64, bool) {
+	min, ok := f.storage.Min()
+	return min / ShardWidth, ok
+}
+
 // rowFilter is a function signature for controlling iteration over containers
 // in a fragment. It will be invoked on each container found and returns two
 // booleans. The first is whether the row this container is in should be
diff --git a/roaring/roaring.go b/roaring/roaring.go
index 7addfc2f4..f7c3feb37 100644
--- a/roaring/roaring.go
+++ b/roaring/roaring.go
@@ -2008,12 +2008,12 @@ func (c *Container) arrayMax() uint16 {
 func (c *Container) bitmapMax() uint16 {
 	// Search bitmap in reverse order.
 	bitmap := c.bitmap()
-	for i := len(bitmap) - 1; i > 0; i-- {
+	for i := len(bitmap); i > 0; i-- {
 		// If value is zero then skip.
-		v := bitmap[i]
+		v := bitmap[i-1]
 		if v != 0 {
 			r := bits.LeadingZeros64(v)
-			return uint16(i*64 + 63 - r)
+			return uint16((i-1)*64 + 63 - r)
 		}
 	}
 	return 0