diff --git a/ddtrace/tracer/sampler.go b/ddtrace/tracer/sampler.go
index b71306c020..57971c63e3 100644
--- a/ddtrace/tracer/sampler.go
+++ b/ddtrace/tracer/sampler.go
@@ -292,6 +292,7 @@ func (rs *rulesSampler) apply(span *span) bool {
 	var matched bool
 	rate := rs.globalRate
 	for _, rule := range rs.rules {
+		fmt.Println("try match", rule.exactService, rule.exactName, span.Service, span.Name)
 		if rule.match(span) {
 			matched = true
 			rate = rule.Rate
diff --git a/ddtrace/tracer/span.go b/ddtrace/tracer/span.go
index e9b3741cbf..32c78628dd 100644
--- a/ddtrace/tracer/span.go
+++ b/ddtrace/tracer/span.go
@@ -373,7 +373,11 @@ func (s *span) finish(finishTime int64) {
 		// client sampling enabled. This will lead to inexact APM metrics but reduces performance impact.
 		keep = false
 	}
-	s.context.finish(keep)
+	if keep {
+		// a single kept span keeps the whole trace.
+		s.context.trace.keep()
+	}
+	s.context.finish()
 }
 
 // newAggregableSpan creates a new summary for the span s, within an application
diff --git a/ddtrace/tracer/spancontext.go b/ddtrace/tracer/spancontext.go
index 399a320e3e..228b688644 100644
--- a/ddtrace/tracer/spancontext.go
+++ b/ddtrace/tracer/spancontext.go
@@ -25,7 +25,7 @@ type spanContext struct {
 
 	trace  *trace // reference to the trace that this span belongs too
 	span   *span  // reference to the span that hosts this context
-	drop   bool   // when true, the span will not be sent to the agent, even when not computing stats in the tracer.
+	drop   bool   // reports whether this span was dropped by the rate sampler
 	errors int64  // number of spans with errors in this trace
 
 	// the below group should propagate cross-process
@@ -126,7 +126,7 @@ func (c *spanContext) baggageItem(key string) string {
 }
 
 // finish marks this span as finished in the trace.
-func (c *spanContext) finish(keep bool) { c.trace.finishedOne(c.span, keep) }
+func (c *spanContext) finish() { c.trace.finishedOne(c.span) }
 
 // trace contains shared context information about a trace, such as sampling
 // priority, the root reference and a buffer of the spans which are part of the
@@ -138,7 +138,7 @@ type trace struct {
 	full     bool         // signifies that the span buffer is full
 	priority *float64     // sampling priority
 	locked   bool         // specifies if the sampling priority can be altered
-	keep bool             // keep indicates whether to send the trace to the agent or no.
+	kept     bool         // kept indicates whether to send the trace to the agent or no.
 
 	// root specifies the root of the trace, if known; it is nil when a span
 	// context is extracted from a carrier, at which point there are no spans in
@@ -180,6 +180,12 @@ func (t *trace) setSamplingPriority(p float64) {
 	t.setSamplingPriorityLocked(p)
 }
 
+func (t *trace) keep() {
+	t.mu.Lock()
+	defer t.mu.Unlock()
+	t.kept = true
+}
+
 func (t *trace) setSamplingPriorityLocked(p float64) {
 	if t.locked {
 		return
@@ -226,7 +232,7 @@ func (t *trace) push(sp *span) {
 // finishedOne aknowledges that another span in the trace has finished, and checks
 // if the trace is complete, in which case it calls the onFinish function. It uses
 // the given priority, if non-nil, to mark the root span.
-func (t *trace) finishedOne(s *span, keep bool) {
+func (t *trace) finishedOne(s *span) {
 	t.mu.Lock()
 	defer t.mu.Unlock()
 	if t.full {
@@ -236,9 +242,6 @@ func (t *trace) finishedOne(s *span, keep bool) {
 		// to a race condition where spans can be modified while flushing.
 		return
 	}
-	if keep {
-		t.keep = true
-	}
 	t.finished++
 	if s == t.root && t.priority != nil {
 		// after the root has finished we lock down the priority;
@@ -254,7 +257,7 @@ func (t *trace) finishedOne(s *span, keep bool) {
 		t.spans = nil
 		t.finished = 0 // important, because a buffer can be used for several flushes
 	}()
-	if !t.keep {
+	if !t.kept {
 		return
 	}
 	if tr, ok := internal.GetGlobalTracer().(*tracer); ok {
diff --git a/ddtrace/tracer/tracer_test.go b/ddtrace/tracer/tracer_test.go
index dc38acf501..d60a3aee71 100644
--- a/ddtrace/tracer/tracer_test.go
+++ b/ddtrace/tracer/tracer_test.go
@@ -236,15 +236,49 @@ func TestTracerStartSpan(t *testing.T) {
 		child := tracer.StartSpan("home/user", Measured(), ChildOf(parent.context)).(*span)
 		assert.Equal(t, 1.0, child.Metrics[keyMeasured])
 	})
+}
 
-	t.Run("sampling_priority", func(t *testing.T) {
-		tracer := newTracer()
+func TestP0Dropping(t *testing.T) {
+	t.Run("p0 are kept by default", func(t *testing.T) {
+		tracer, _, _, stop := startTestTracer(t)
+		defer stop()
+		tracer.prioritySampling.defaultRate = 0
 		tracer.config.serviceName = "test_service"
-		tracer.rulesSampling.rules = append(tracer.rulesSampling.rules, SamplingRule{exactService: "test_service", exactName: "web.request", Rate: 1})
-		span := tracer.StartSpan("web.request").(*span)
-		assert.Equal(t, float64(ext.PriorityAutoKeep), span.Metrics[keySamplingPriority])
-		priority, _ := span.context.samplingPriority()
-		assert.Equal(t, 1, priority)
+		span := tracer.StartSpan("name_1").(*span)
+		child := tracer.StartSpan("name_2", ChildOf(span.context))
+		child.Finish()
+		span.Finish()
+		assert.Equal(t, float64(ext.PriorityAutoReject), span.Metrics[keySamplingPriority])
+		assert.True(t, span.context.trace.kept)
+	})
+
+	t.Run("p0 are dropped when DropP0s flag is on", func(t *testing.T) {
+		tracer, _, _, stop := startTestTracer(t)
+		defer stop()
+		tracer.features.DropP0s = true
+		tracer.prioritySampling.defaultRate = 0
+		tracer.config.serviceName = "test_service"
+		span := tracer.StartSpan("name_1").(*span)
+		child := tracer.StartSpan("name_2", ChildOf(span.context))
+		child.Finish()
+		span.Finish()
+		assert.Equal(t, float64(ext.PriorityAutoReject), span.Metrics[keySamplingPriority])
+		assert.False(t, span.context.trace.kept)
+	})
+
+	t.Run("p0 are kept if at least one span should be kept", func(t *testing.T) {
+		tracer, _, _, stop := startTestTracer(t)
+		defer stop()
+		tracer.features.DropP0s = true
+		tracer.prioritySampling.defaultRate = 0
+		tracer.config.serviceName = "test_service"
+		span := tracer.StartSpan("name_1").(*span)
+		child := tracer.StartSpan("name_2", ChildOf(span.context))
+		child.SetTag(ext.EventSampleRate, 1)
+		child.Finish()
+		span.Finish()
+		assert.Equal(t, float64(ext.PriorityAutoReject), span.Metrics[keySamplingPriority])
+		assert.True(t, span.context.trace.kept)
 	})
 }