diff --git a/model/textparse/openmetricsparse.go b/model/textparse/openmetricsparse.go
index 0fe801087..c17d40020 100644
--- a/model/textparse/openmetricsparse.go
+++ b/model/textparse/openmetricsparse.go
@@ -17,7 +17,6 @@
 package textparse
 
 import (
-	"bytes"
 	"errors"
 	"fmt"
 	"io"
@@ -31,8 +30,6 @@ import (
 	"github.com/prometheus/prometheus/model/value"
 )
 
-var allowedSuffixes = [][]byte{[]byte("_total"), []byte("_bucket")}
-
 type openMetricsLexer struct {
 	b     []byte
 	i     int
@@ -364,12 +361,6 @@ func (p *OpenMetricsParser) Next() (Entry, error) {
 }
 
 func (p *OpenMetricsParser) parseComment() error {
-	// Validate the name of the metric. It must have _total or _bucket as
-	// suffix for exemplars to be supported.
-	if err := p.validateNameForExemplar(p.series[:p.offsets[0]-p.start]); err != nil {
-		return err
-	}
-
 	var err error
 	// Parse the labels.
 	p.eOffsets, err = p.parseLVals(p.eOffsets)
@@ -474,12 +465,3 @@ func (p *OpenMetricsParser) getFloatValue(t token, after string) (float64, error
 	}
 	return val, nil
 }
-
-func (p *OpenMetricsParser) validateNameForExemplar(name []byte) error {
-	for _, suffix := range allowedSuffixes {
-		if bytes.HasSuffix(name, suffix) {
-			return nil
-		}
-	}
-	return fmt.Errorf("metric name %v does not support exemplars", string(name))
-}
diff --git a/model/textparse/openmetricsparse_test.go b/model/textparse/openmetricsparse_test.go
index 12fb03f01..d65e4977e 100644
--- a/model/textparse/openmetricsparse_test.go
+++ b/model/textparse/openmetricsparse_test.go
@@ -45,9 +45,14 @@ hh_bucket{le="+Inf"} 1
 # TYPE gh gaugehistogram
 gh_bucket{le="+Inf"} 1
 # TYPE hhh histogram
-hhh_bucket{le="+Inf"} 1 # {aa="bb"} 4
+hhh_bucket{le="+Inf"} 1 # {id="histogram-bucket-test"} 4
+hhh_count 1 # {id="histogram-count-test"} 4
 # TYPE ggh gaugehistogram
-ggh_bucket{le="+Inf"} 1 # {cc="dd",xx="yy"} 4 123.123
+ggh_bucket{le="+Inf"} 1 # {id="gaugehistogram-bucket-test",xx="yy"} 4 123.123
+ggh_count 1 # {id="gaugehistogram-count-test",xx="yy"} 4 123.123
+# TYPE smr_seconds summary
+smr_seconds_count 2.0 # {id="summary-count-test"} 1 123.321
+smr_seconds_sum 42.0 # {id="summary-sum-test"} 1 123.321
 # TYPE ii info
 ii{foo="bar"} 1
 # TYPE ss stateset
@@ -59,7 +64,7 @@ _metric_starting_with_underscore 1
 testmetric{_label_starting_with_underscore="foo"} 1
 testmetric{label="\"bar\""} 1
 # TYPE foo counter
-foo_total 17.0 1520879607.789 # {xx="yy"} 5`
+foo_total 17.0 1520879607.789 # {id="counter-test"} 5`
 
 	input += "\n# HELP metric foo\x00bar"
 	input += "\nnull_byte_metric{a=\"abc\x00\"} 1"
@@ -152,7 +157,12 @@ foo_total 17.0 1520879607.789 # {xx="yy"} 5`
 			m:    `hhh_bucket{le="+Inf"}`,
 			v:    1,
 			lset: labels.FromStrings("__name__", "hhh_bucket", "le", "+Inf"),
-			e:    &exemplar.Exemplar{Labels: labels.FromStrings("aa", "bb"), Value: 4},
+			e:    &exemplar.Exemplar{Labels: labels.FromStrings("id", "histogram-bucket-test"), Value: 4},
+		}, {
+			m:    `hhh_count`,
+			v:    1,
+			lset: labels.FromStrings("__name__", "hhh_count"),
+			e:    &exemplar.Exemplar{Labels: labels.FromStrings("id", "histogram-count-test"), Value: 4},
 		}, {
 			m:   "ggh",
 			typ: MetricTypeGaugeHistogram,
@@ -160,7 +170,25 @@ foo_total 17.0 1520879607.789 # {xx="yy"} 5`
 			m:    `ggh_bucket{le="+Inf"}`,
 			v:    1,
 			lset: labels.FromStrings("__name__", "ggh_bucket", "le", "+Inf"),
-			e:    &exemplar.Exemplar{Labels: labels.FromStrings("cc", "dd", "xx", "yy"), Value: 4, HasTs: true, Ts: 123123},
+			e:    &exemplar.Exemplar{Labels: labels.FromStrings("id", "gaugehistogram-bucket-test", "xx", "yy"), Value: 4, HasTs: true, Ts: 123123},
+		}, {
+			m:    `ggh_count`,
+			v:    1,
+			lset: labels.FromStrings("__name__", "ggh_count"),
+			e:    &exemplar.Exemplar{Labels: labels.FromStrings("id", "gaugehistogram-count-test", "xx", "yy"), Value: 4, HasTs: true, Ts: 123123},
+		}, {
+			m:   "smr_seconds",
+			typ: MetricTypeSummary,
+		}, {
+			m:    `smr_seconds_count`,
+			v:    2,
+			lset: labels.FromStrings("__name__", "smr_seconds_count"),
+			e:    &exemplar.Exemplar{Labels: labels.FromStrings("id", "summary-count-test"), Value: 1, HasTs: true, Ts: 123321},
+		}, {
+			m:    `smr_seconds_sum`,
+			v:    42,
+			lset: labels.FromStrings("__name__", "smr_seconds_sum"),
+			e:    &exemplar.Exemplar{Labels: labels.FromStrings("id", "summary-sum-test"), Value: 1, HasTs: true, Ts: 123321},
 		}, {
 			m:   "ii",
 			typ: MetricTypeInfo,
@@ -206,7 +234,7 @@ foo_total 17.0 1520879607.789 # {xx="yy"} 5`
 			v:    17,
 			lset: labels.FromStrings("__name__", "foo_total"),
 			t:    int64p(1520879607789),
-			e:    &exemplar.Exemplar{Labels: labels.FromStrings("xx", "yy"), Value: 5},
+			e:    &exemplar.Exemplar{Labels: labels.FromStrings("id", "counter-test"), Value: 5},
 		}, {
 			m:    "metric",
 			help: "foo\x00bar",
@@ -495,10 +523,6 @@ func TestOpenMetricsParseErrors(t *testing.T) {
 			input: `custom_metric_total 1 # {aa="bb"}`,
 			err:   "expected value after exemplar labels, got \"}\" (\"EOF\") while parsing: \"custom_metric_total 1 # {aa=\\\"bb\\\"}\"",
 		},
-		{
-			input: `custom_metric 1 # {aa="bb"}`,
-			err:   "metric name custom_metric does not support exemplars",
-		},
 		{
 			input: `custom_metric_total 1 # {aa="bb",,cc="dd"} 1`,
 			err:   "expected label name, got \",c\" (\"COMMA\") while parsing: \"custom_metric_total 1 # {aa=\\\"bb\\\",,c\"",