diff --git a/pkg/trace/api/info.go b/pkg/trace/api/info.go
index 4ea4a5e5bb5093..79d1d55d7d5eea 100644
--- a/pkg/trace/api/info.go
+++ b/pkg/trace/api/info.go
@@ -10,8 +10,10 @@ import (
 	"encoding/json"
 	"fmt"
 	"net/http"
+	"slices"
 
 	"github.com/DataDog/datadog-agent/pkg/obfuscate"
+	"github.com/DataDog/datadog-agent/pkg/trace/stats"
 )
 
 // makeInfoHandler returns a new handler for handling the discovery endpoint.
@@ -61,6 +63,17 @@ func (r *HTTPReceiver) makeInfoHandler() (hash string, handler http.HandlerFunc)
 		oconf.Redis = o.Redis
 		oconf.Memcached = o.Memcached
 	}
+
+	// We check that endpoints contains stats, even though we know this version of the
+	// agent supports it. It's conceivable that the stats endpoint could be disabled at some point
+	// so this is defensive against that case.
+	canDropP0 := !r.conf.ProbabilisticSamplerEnabled && slices.Contains(all, "/v0.6/stats")
+
+	var spanKindsStatsComputed []string
+	if r.conf.ComputeStatsBySpanKind {
+		spanKindsStatsComputed = stats.KindsComputed
+	}
+
 	txt, err := json.MarshalIndent(struct {
 		Version                string        `json:"version"`
 		GitCommit              string        `json:"git_commit"`
@@ -72,15 +85,17 @@ func (r *HTTPReceiver) makeInfoHandler() (hash string, handler http.HandlerFunc)
 		EvpProxyAllowedHeaders []string      `json:"evp_proxy_allowed_headers"`
 		Config                 reducedConfig `json:"config"`
 		PeerTags               []string      `json:"peer_tags"`
+		SpanKindsStatsComputed []string      `json:"span_kinds_stats_computed"`
 	}{
 		Version:                r.conf.AgentVersion,
 		GitCommit:              r.conf.GitCommit,
 		Endpoints:              all,
 		FeatureFlags:           r.conf.AllFeatures(),
-		ClientDropP0s:          true,
+		ClientDropP0s:          canDropP0,
 		SpanMetaStructs:        true,
 		LongRunningSpans:       true,
 		EvpProxyAllowedHeaders: EvpProxyAllowedHeaders,
+		SpanKindsStatsComputed: spanKindsStatsComputed,
 		Config: reducedConfig{
 			DefaultEnv:             r.conf.DefaultEnv,
 			TargetTPS:              r.conf.TargetTPS,
diff --git a/pkg/trace/api/info_test.go b/pkg/trace/api/info_test.go
index 0d82e3fd41b2c2..d8fc856b6a6bed 100644
--- a/pkg/trace/api/info_test.go
+++ b/pkg/trace/api/info_test.go
@@ -302,6 +302,7 @@ func TestInfoHandler(t *testing.T) {
 		"long_running_spans":        nil,
 		"evp_proxy_allowed_headers": nil,
 		"peer_tags":                 nil,
+		"span_kinds_stats_computed": nil,
 		"config": map[string]interface{}{
 			"default_env":               nil,
 			"target_tps":                nil,
diff --git a/pkg/trace/stats/span_concentrator.go b/pkg/trace/stats/span_concentrator.go
index d886b9e7495f7c..e48f937f267a5a 100644
--- a/pkg/trace/stats/span_concentrator.go
+++ b/pkg/trace/stats/span_concentrator.go
@@ -6,6 +6,7 @@
 package stats
 
 import (
+	"slices"
 	"strings"
 	"sync"
 	"time"
@@ -159,12 +160,16 @@ func (sc *SpanConcentrator) NewStatSpan(
 // computeStatsForSpanKind returns true if the span.kind value makes the span eligible for stats computation.
 func computeStatsForSpanKind(kind string) bool {
 	k := strings.ToLower(kind)
-	switch k {
-	case "server", "consumer", "client", "producer":
-		return true
-	default:
-		return false
-	}
+	return slices.Contains(KindsComputed, k)
+}
+
+// KindsComputed is the list of span kinds that will have stats computed on them
+// when computeStatsByKind is enabled in the concentrator.
+var KindsComputed = []string{
+	"server",
+	"consumer",
+	"client",
+	"producer",
 }
 
 func (sc *SpanConcentrator) addSpan(s *StatSpan, aggKey PayloadAggregationKey, containerID string, containerTags []string, origin string, weight float64) {