diff --git a/cmd/thanos/compact.go b/cmd/thanos/compact.go
index dd462d6b51..c95cf113d6 100644
--- a/cmd/thanos/compact.go
+++ b/cmd/thanos/compact.go
@@ -66,6 +66,9 @@ func registerCompact(m map[string]setupFunc, app *kingpin.Application, name stri
 
 	haltOnError := cmd.Flag("debug.halt-on-error", "Halt the process if a critical compaction error is detected.").
 		Hidden().Default("true").Bool()
+	acceptMalformedIndex := cmd.Flag("debug.accept-malformed-index",
+		"Compaction index verification will ignore out of order label names.").
+		Hidden().Default("false").Bool()
 
 	httpAddr := regHTTPAddrFlag(cmd)
 
@@ -102,6 +105,7 @@ func registerCompact(m map[string]setupFunc, app *kingpin.Application, name stri
 			objStoreConfig,
 			time.Duration(*syncDelay),
 			*haltOnError,
+			*acceptMalformedIndex,
 			*wait,
 			map[compact.ResolutionLevel]time.Duration{
 				compact.ResolutionLevelRaw: time.Duration(*retentionRaw),
@@ -125,6 +129,7 @@ func runCompact(
 	objStoreConfig *pathOrContent,
 	syncDelay time.Duration,
 	haltOnError bool,
+	acceptMalformedIndex bool,
 	wait bool,
 	retentionByResolution map[compact.ResolutionLevel]time.Duration,
 	component string,
@@ -162,7 +167,8 @@ func runCompact(
 		}
 	}()
 
-	sy, err := compact.NewSyncer(logger, reg, bkt, syncDelay, blockSyncConcurrency)
+	sy, err := compact.NewSyncer(logger, reg, bkt, syncDelay,
+		blockSyncConcurrency, acceptMalformedIndex)
 	if err != nil {
 		return errors.Wrap(err, "create syncer")
 	}
diff --git a/pkg/block/index.go b/pkg/block/index.go
index 232bf40d37..777654f2e6 100644
--- a/pkg/block/index.go
+++ b/pkg/block/index.go
@@ -16,6 +16,7 @@ import (
 	"github.com/prometheus/tsdb/fileutil"
 
 	"github.com/go-kit/kit/log"
+	"github.com/go-kit/kit/log/level"
 	"github.com/improbable-eng/thanos/pkg/runutil"
 	"github.com/oklog/ulid"
 	"github.com/pkg/errors"
@@ -248,6 +249,20 @@ type Stats struct {
 	// Specifically we mean here chunks with minTime == block.maxTime and maxTime > block.MaxTime. These are
 	// are segregated into separate counters. These chunks are safe to be deleted, since they are duplicated across 2 blocks.
 	Issue347OutsideChunks int
+	// OutOfOrderLabels represents the number of postings that contained out
+	// of order labels, a bug present in Prometheus 2.8.0 and below.
+	OutOfOrderLabels int
+}
+
+// PrometheusIssue5372Err returns an error if the Stats object indicates
+// postings with out of order labels.  This is corrected by Prometheus Issue
+// #5372 and affects Prometheus versions 2.8.0 and below.
+func (i Stats) PrometheusIssue5372Err() error {
+	if i.OutOfOrderLabels > 0 {
+		return errors.Errorf("index contains %d postings with out of order labels",
+			i.OutOfOrderLabels)
+	}
+	return nil
 }
 
 // Issue347OutsideChunksErr returns error if stats indicates issue347 block issue, that is repaired explicitly before compaction (on plan block).
@@ -301,6 +316,10 @@ func (i Stats) AnyErr() error {
 		errMsg = append(errMsg, err.Error())
 	}
 
+	if err := i.PrometheusIssue5372Err(); err != nil {
+		errMsg = append(errMsg, err.Error())
+	}
+
 	if len(errMsg) > 0 {
 		return errors.New(strings.Join(errMsg, ", "))
 	}
@@ -348,7 +367,12 @@ func GatherIndexIssueStats(logger log.Logger, fn string, minTime int64, maxTime
 		l0 := lset[0]
 		for _, l := range lset[1:] {
 			if l.Name < l0.Name {
-				return stats, errors.Errorf("out-of-order label set %s for series %d", lset, id)
+				stats.OutOfOrderLabels++
+				level.Warn(logger).Log("msg",
+					"out-of-order label set: known bug in Prometheus 2.8.0 and below",
+					"labelset", fmt.Sprintf("%s", lset),
+					"series", fmt.Sprintf("%d", id),
+				)
 			}
 			l0 = l
 		}
diff --git a/pkg/compact/compact.go b/pkg/compact/compact.go
index ca05adfb4a..6fd89b76e9 100644
--- a/pkg/compact/compact.go
+++ b/pkg/compact/compact.go
@@ -47,6 +47,7 @@ type Syncer struct {
 	blocksMtx            sync.Mutex
 	blockSyncConcurrency int
 	metrics              *syncerMetrics
+	acceptMalformedIndex bool
 }
 
 type syncerMetrics struct {
@@ -128,7 +129,7 @@ func newSyncerMetrics(reg prometheus.Registerer) *syncerMetrics {
 
 // NewSyncer returns a new Syncer for the given Bucket and directory.
 // Blocks must be at least as old as the sync delay for being considered.
-func NewSyncer(logger log.Logger, reg prometheus.Registerer, bkt objstore.Bucket, syncDelay time.Duration, blockSyncConcurrency int) (*Syncer, error) {
+func NewSyncer(logger log.Logger, reg prometheus.Registerer, bkt objstore.Bucket, syncDelay time.Duration, blockSyncConcurrency int, acceptMalformedIndex bool) (*Syncer, error) {
 	if logger == nil {
 		logger = log.NewNopLogger()
 	}
@@ -140,6 +141,7 @@ func NewSyncer(logger log.Logger, reg prometheus.Registerer, bkt objstore.Bucket
 		bkt:                  bkt,
 		metrics:              newSyncerMetrics(reg),
 		blockSyncConcurrency: blockSyncConcurrency,
+		acceptMalformedIndex: acceptMalformedIndex,
 	}, nil
 }
 
@@ -291,6 +293,7 @@ func (c *Syncer) Groups() (res []*Group, err error) {
 				c.bkt,
 				labels.FromMap(m.Thanos.Labels),
 				m.Thanos.Downsample.Resolution,
+				c.acceptMalformedIndex,
 				c.metrics.compactions.WithLabelValues(GroupKey(*m)),
 				c.metrics.compactionFailures.WithLabelValues(GroupKey(*m)),
 				c.metrics.garbageCollectedBlocks,
@@ -436,6 +439,7 @@ type Group struct {
 	resolution                  int64
 	mtx                         sync.Mutex
 	blocks                      map[ulid.ULID]*metadata.Meta
+	acceptMalformedIndex        bool
 	compactions                 prometheus.Counter
 	compactionFailures          prometheus.Counter
 	groupGarbageCollectedBlocks prometheus.Counter
@@ -447,6 +451,7 @@ func newGroup(
 	bkt objstore.Bucket,
 	lset labels.Labels,
 	resolution int64,
+	acceptMalformedIndex bool,
 	compactions prometheus.Counter,
 	compactionFailures prometheus.Counter,
 	groupGarbageCollectedBlocks prometheus.Counter,
@@ -460,6 +465,7 @@ func newGroup(
 		labels:                      lset,
 		resolution:                  resolution,
 		blocks:                      map[ulid.ULID]*metadata.Meta{},
+		acceptMalformedIndex:        acceptMalformedIndex,
 		compactions:                 compactions,
 		compactionFailures:          compactionFailures,
 		groupGarbageCollectedBlocks: groupGarbageCollectedBlocks,
@@ -769,6 +775,11 @@ func (cg *Group) compact(ctx context.Context, dir string, comp tsdb.Compactor) (
 		if err := stats.Issue347OutsideChunksErr(); err != nil {
 			return false, ulid.ULID{}, issue347Error(errors.Wrapf(err, "invalid, but reparable block %s", pdir), meta.ULID)
 		}
+
+		if err := stats.PrometheusIssue5372Err(); !cg.acceptMalformedIndex && err != nil {
+			return false, ulid.ULID{}, errors.Wrapf(err,
+				"block id %s, try running with --debug.accept-malformed-index", id)
+		}
 	}
 	level.Debug(cg.logger).Log("msg", "downloaded and verified blocks",
 		"blocks", fmt.Sprintf("%v", plan), "duration", time.Since(begin))
@@ -816,7 +827,7 @@ func (cg *Group) compact(ctx context.Context, dir string, comp tsdb.Compactor) (
 	}
 
 	// Ensure the output block is valid.
-	if err := block.VerifyIndex(cg.logger, filepath.Join(bdir, block.IndexFilename), newMeta.MinTime, newMeta.MaxTime); err != nil {
+	if err := block.VerifyIndex(cg.logger, filepath.Join(bdir, block.IndexFilename), newMeta.MinTime, newMeta.MaxTime); !cg.acceptMalformedIndex && err != nil {
 		return false, ulid.ULID{}, halt(errors.Wrapf(err, "invalid result block %s", bdir))
 	}
 
diff --git a/pkg/compact/compact_e2e_test.go b/pkg/compact/compact_e2e_test.go
index 6f2194c41f..738048c5c2 100644
--- a/pkg/compact/compact_e2e_test.go
+++ b/pkg/compact/compact_e2e_test.go
@@ -32,7 +32,7 @@ func TestSyncer_SyncMetas_e2e(t *testing.T) {
 		ctx, cancel := context.WithTimeout(context.Background(), 120*time.Second)
 		defer cancel()
 
-		sy, err := NewSyncer(nil, nil, bkt, 0, 1)
+		sy, err := NewSyncer(nil, nil, bkt, 0, 1, false)
 		testutil.Ok(t, err)
 
 		// Generate 15 blocks. Initially the first 10 are synced into memory and only the last
@@ -134,7 +134,7 @@ func TestSyncer_GarbageCollect_e2e(t *testing.T) {
 		}
 
 		// Do one initial synchronization with the bucket.
-		sy, err := NewSyncer(nil, nil, bkt, 0, 1)
+		sy, err := NewSyncer(nil, nil, bkt, 0, 1, false)
 		testutil.Ok(t, err)
 		testutil.Ok(t, sy.SyncMetas(ctx))
 
@@ -244,6 +244,7 @@ func TestGroup_Compact_e2e(t *testing.T) {
 			bkt,
 			extLset,
 			124,
+			false,
 			metrics.compactions.WithLabelValues(""),
 			metrics.compactionFailures.WithLabelValues(""),
 			metrics.garbageCollectedBlocks,