diff --git a/spring-cloud-sleuth-core/src/main/java/org/springframework/cloud/sleuth/Span.java b/spring-cloud-sleuth-core/src/main/java/org/springframework/cloud/sleuth/Span.java
index 29b8a0d59..522493b76 100644
--- a/spring-cloud-sleuth-core/src/main/java/org/springframework/cloud/sleuth/Span.java
+++ b/spring-cloud-sleuth-core/src/main/java/org/springframework/cloud/sleuth/Span.java
@@ -190,7 +190,7 @@ public class Span {
 			this.startNanos = null; // don't know the start tick
 			this.begin = begin;
 		} else {
-			this.startNanos = System.nanoTime();
+			this.startNanos = nanoTime();
 			this.begin = System.currentTimeMillis();
 		}
 		if (end > 0) {
@@ -226,7 +226,7 @@ public class Span {
 				this.end = System.currentTimeMillis();
 			}
 			if (this.startNanos != null) { // set a precise duration
-				this.durationMicros = (System.nanoTime() - this.startNanos) / 1000;
+				this.durationMicros = Math.max(1, (nanoTime() - this.startNanos) / 1000);
 			} else {
 				this.durationMicros = (this.end - this.begin) * 1000;
 			}
@@ -248,6 +248,8 @@ public class Span {
 	/**
 	 * Return the total amount of time elapsed since start was called, if running, or
 	 * difference between stop and start, in microseconds.
+	 *
+	 * @return zero if not running, or a positive number of microseconds.
 	 */
 	@JsonIgnore
 	public synchronized long getAccumulatedMicros() {
@@ -258,13 +260,19 @@ public class Span {
 				return 0;
 			}
 			if (this.startNanos != null) {
-				return (System.nanoTime() - this.startNanos) / 1000;
+				return Math.max(1, (nanoTime() - this.startNanos) / 1000);
 			} else  {
 				return (System.currentTimeMillis() - this.begin) * 1000;
 			}
 		}
 	}
 
+	// Visible for testing
+	@JsonIgnore
+	long nanoTime() {
+		return System.nanoTime();
+	}
+
 	/**
 	 * Has the span been started and not yet stopped?
 	 */
diff --git a/spring-cloud-sleuth-core/src/test/java/org/springframework/cloud/sleuth/SpanTests.java b/spring-cloud-sleuth-core/src/test/java/org/springframework/cloud/sleuth/SpanTests.java
index 1021a6213..8f80bc15a 100644
--- a/spring-cloud-sleuth-core/src/test/java/org/springframework/cloud/sleuth/SpanTests.java
+++ b/spring-cloud-sleuth-core/src/test/java/org/springframework/cloud/sleuth/SpanTests.java
@@ -18,6 +18,7 @@ package org.springframework.cloud.sleuth;
 
 import java.io.IOException;
 import java.util.Collections;
+import java.util.concurrent.atomic.AtomicLong;
 
 import com.fasterxml.jackson.core.JsonProcessingException;
 import com.fasterxml.jackson.databind.ObjectMapper;
@@ -135,4 +136,43 @@ public class SpanTests {
 		assertThat(deserialized.getAccumulatedMicros())
 				.isEqualTo(span.getAccumulatedMicros());
 	}
+
+	// Duration of 0 is confusing to plot and can be misinterpreted as null
+	@Test public void getAccumulatedMicros_roundsUpToOneWhenRunning() throws IOException {
+		AtomicLong nanoTime = new AtomicLong();
+
+		// starts the span, recording its initial tick as zero
+		Span span = new Span(0, 0, "http:name", 1L, Collections.<Long>emptyList(), 2L, true,
+				true, "process", null) {
+			@Override long nanoTime() {
+				return nanoTime.get();
+			}
+		};
+
+		// When only 100 nanoseconds passed
+		nanoTime.set(100L);
+
+		// We round so that we don't confuse "not started" with a short span.
+		assertThat(span.getAccumulatedMicros()).isEqualTo(1L);
+	}
+
+	// Duration of 0 is confusing to plot and can be misinterpreted as null
+	@Test public void getAccumulatedMicros_roundsUpToOneWhenStopped() throws IOException {
+		AtomicLong nanoTime = new AtomicLong();
+
+		// starts the span, recording its initial tick as zero
+		Span span = new Span(0, 0, "http:name", 1L, Collections.<Long>emptyList(), 2L, true,
+				true, "process", null) {
+			@Override long nanoTime() {
+				return nanoTime.get();
+			}
+		};
+
+		// When only 100 nanoseconds passed
+		nanoTime.set(100L);
+		span.stop();
+
+		// We round so that we don't confuse "not started" with a short span.
+		assertThat(span.getAccumulatedMicros()).isEqualTo(1L);
+	}
 }
diff --git a/spring-cloud-sleuth-dependencies/pom.xml b/spring-cloud-sleuth-dependencies/pom.xml
index 585448591..3e1c80af7 100644
--- a/spring-cloud-sleuth-dependencies/pom.xml
+++ b/spring-cloud-sleuth-dependencies/pom.xml
@@ -16,7 +16,7 @@
 	<properties>
 		<spring-cloud-netflix.version>1.2.0.BUILD-SNAPSHOT</spring-cloud-netflix.version>
 		<aspectj.version>1.8.4</aspectj.version>
-		<zipkin.version>1.1.5</zipkin.version>
+		<zipkin.version>1.3.0</zipkin.version>
 	</properties>
 	<dependencyManagement>
 		<dependencies>
diff --git a/spring-cloud-sleuth-samples/pom.xml b/spring-cloud-sleuth-samples/pom.xml
index 65e702ae6..9da6ef988 100644
--- a/spring-cloud-sleuth-samples/pom.xml
+++ b/spring-cloud-sleuth-samples/pom.xml
@@ -59,12 +59,12 @@
 			<dependency>
 				<groupId>io.zipkin.java</groupId>
 				<artifactId>zipkin</artifactId>
-				<version>1.1.5</version>
+				<version>1.3.0</version>
 			</dependency>
 			<dependency>
 				<groupId>io.zipkin.java</groupId>
 				<artifactId>zipkin-server</artifactId>
-				<version>1.1.5</version>
+				<version>1.3.0</version>
 			</dependency>
 		</dependencies>
 	</dependencyManagement>