diff --git a/scripts/base/frameworks/sumstats/plugins/hll_unique.bro b/scripts/base/frameworks/sumstats/plugins/hll_unique.bro
index 56595ca434..1110e6e105 100644
--- a/scripts/base/frameworks/sumstats/plugins/hll_unique.bro
+++ b/scripts/base/frameworks/sumstats/plugins/hll_unique.bro
@@ -4,8 +4,11 @@ module SumStats;
 
 export {
 	redef record Reducer += {
-		## The threshold when we switch to hll
+		## The error margin for HLL.
 		hll_error_margin: double &default=0.01;
+	
+		## The confidence for for HLL.
+		hll_confidence: double &default=0.95;
 	};
 
 	redef enum Calculation += {
@@ -26,8 +29,9 @@ redef record ResultVal += {
 	# specialized bifs.
 	card: opaque of cardinality &optional;
 
-	# We need this in the compose hook.
+	# We need these in the compose hook.
 	hll_error_margin: double &optional;
+	hll_confidence: double &optional;
 };
 
 hook register_observe_plugins()
@@ -36,8 +40,9 @@ hook register_observe_plugins()
 		{
 		if ( ! rv?$card )
 			{
-			rv$card = hll_cardinality_init(r$hll_error_margin);
+			rv$card = hll_cardinality_init(r$hll_error_margin, r$hll_confidence);
 			rv$hll_error_margin = r$hll_error_margin;
+			rv$hll_confidence = r$hll_confidence;
 			rv$hll_unique = 0;
 			}
 
@@ -48,7 +53,7 @@ hook register_observe_plugins()
 
 hook compose_resultvals_hook(result: ResultVal, rv1: ResultVal, rv2: ResultVal)
 	{
-	local rhll = hll_cardinality_init(rv1$hll_error_margin);
+	local rhll = hll_cardinality_init(rv1$hll_error_margin, rv1$hll_confidence);
 	hll_cardinality_merge_into(rhll, rv1$card);
 	hll_cardinality_merge_into(rhll, rv2$card);
 
diff --git a/src/OpaqueVal.cc b/src/OpaqueVal.cc
index d9999c148b..b7ccd770ce 100644
--- a/src/OpaqueVal.cc
+++ b/src/OpaqueVal.cc
@@ -5,7 +5,7 @@
 #include "Reporter.h"
 #include "Serializer.h"
 #include "probabilistic/BloomFilter.h"
-#include "probabilistic/HyperLogLog.h"
+#include "probabilistic/CardinalityCounter.h"
 
 bool HashVal::IsValid() const
 	{
diff --git a/src/probabilistic/CardinalityCounter.cc b/src/probabilistic/CardinalityCounter.cc
index 5f6b60d0a7..91686bbb69 100644
--- a/src/probabilistic/CardinalityCounter.cc
+++ b/src/probabilistic/CardinalityCounter.cc
@@ -10,7 +10,7 @@
 
 using namespace probabilistic;
 
-int CardinalityCounter::OptimalB(double error)
+int CardinalityCounter::OptimalB(double error, double confidence)
 	{
 	double initial_estimate = 2 * (log(1.04) - log(error)) / log(2);
 	int answer = (int) floor(initial_estimate);
@@ -20,7 +20,7 @@ int CardinalityCounter::OptimalB(double error)
 	do {
 		answer++;
 		k = pow(2, (answer - initial_estimate) / 2);
-	} while ( erf(k / sqrt(2)) < HLL_CONF );
+	} while ( erf(k / sqrt(2)) < confidence );
 
 	return answer;
 	}
@@ -30,6 +30,9 @@ void CardinalityCounter::Init(uint64 size)
 	m = size;
 	buckets = new uint8_t[m];
 
+	// The following magic values are taken directly out of the
+	// description of the HyperLogLog algorithn.
+
 	if ( m == 16 )
 		alpha_m = 0.673;
 
@@ -51,9 +54,9 @@ void CardinalityCounter::Init(uint64 size)
 	V = m;
 	}
 
-CardinalityCounter::CardinalityCounter(double error_margin)
+CardinalityCounter::CardinalityCounter(double error_margin, double confidence)
 	{
-	int b = OptimalB(error_margin);
+	int b = OptimalB(error_margin, confidence);
 	Init((uint64) pow(2, b));
 	}
 
diff --git a/src/probabilistic/CardinalityCounter.h b/src/probabilistic/CardinalityCounter.h
index 909de7a153..6e1c444d95 100644
--- a/src/probabilistic/CardinalityCounter.h
+++ b/src/probabilistic/CardinalityCounter.h
@@ -14,18 +14,24 @@ namespace probabilistic {
 class CardinalityCounter {
 public:
 	/**
-	* Constructor.
-	*
-	* Based on the error_margin, the number of buckets that need to be
-	* kept will be determined. Based on the max_size, the number of bits
-	* that will be used from the hash function will be determined.
-	*
-	* We need the hash function to return integers that are uniformly
-	* distributed from 0 to 2^L-1. And if that happens, the maximum
-	* cardinality that this counter can handle is approximately 2^L. By
-	* default, we will assume a value of 64 bits.
-	*/
-	CardinalityCounter(double error_margin);
+	 * Constructor.
+	 *
+	 * Based on the error_margin, the number of buckets that need to be
+	 * kept will be determined. Based on the max_size, the number of bits
+	 * that will be used from the hash function will be determined.
+	 *
+	 * We need the hash function to return integers that are uniformly
+	 * distributed from 0 to 2^L-1. And if that happens, the maximum
+	 * cardinality that this counter can handle is approximately 2^L. By
+	 * default, we will assume a value of 64 bits.
+	 *
+	 * Confidence in the estimate given by a cardinality counter is.
+	 *
+	 * In other words, if the cardinality is estimated to be 100 with 2%
+	 * error margin and HLL_CONFis 0.95, then we are 95% sure that the
+	 * actual cardinality is between 98 and 102.
+	 */
+	CardinalityCounter(double error_margin, double confidence = 0.95);
 
 	/**
 	* Constructor used for cloning.
@@ -117,8 +123,10 @@ private:
 	 *
 	 * k is the number of standard deviations that we have to go to have
 	 * a confidence level of conf.
+	 *
+	 * confidence: TODO.
 	 */
-	int OptimalB(double error);
+	int OptimalB(double error, double confidence);
 
 	/**
 	* Computes when the first one appears in the element. It looks at the
@@ -128,15 +136,6 @@ private:
 	*/
 	uint8_t Rank(uint64 hash_modified);
 
-	/**
-	 * Confidence in the estimate given by a cardinality counter is.
-	 *
-	 * In other words, if the cardinality is estimated to be 100 with 2%
-	 * error margin and HLL_CONFis 0.95, then we are 95% sure that the
-	 * actual cardinality is between 98 and 102.
-	 */
-	static const double HLL_CONF = .95;
-
 	/**
 	 * This is the number of buckets that will be stored. The standard
 	 * error is 1.04/sqrt(m), so the actual cardinality will be the
diff --git a/src/probabilistic/cardinality-counter.bif b/src/probabilistic/cardinality-counter.bif
index 28f886ff6c..1ec07529dc 100644
--- a/src/probabilistic/cardinality-counter.bif
+++ b/src/probabilistic/cardinality-counter.bif
@@ -16,14 +16,16 @@ module GLOBAL;
 ## Initializes a probabilistic cardinality counter that uses the HyperLogLog algorithm.
 ##
 ## err: the desired error rate (e.g. 0.01).
+## 
+## confidence: the desirec confidence for the error rate (e.g., 0.95).
 ##
 ## Returns: a HLL cardinality handle.
 ##
 ## .. bro:see:: hll_cardinality_estimate hll_cardinality_merge_into hll_cardinality_add
 ##    hll_cardinality_copy
-function hll_cardinality_init%(err: double%): opaque of cardinality
+function hll_cardinality_init%(err: double, confidence: double%): opaque of cardinality
 	%{
-	CardinalityCounter* c = new CardinalityCounter(err);
+	CardinalityCounter* c = new CardinalityCounter(err, confidence);
 	CardinalityVal* cv = new CardinalityVal(c);
 
 	return cv;
diff --git a/testing/btest/bifs/hll_cardinality.bro b/testing/btest/bifs/hll_cardinality.bro
index 96371d268f..d1b0807416 100644
--- a/testing/btest/bifs/hll_cardinality.bro
+++ b/testing/btest/bifs/hll_cardinality.bro
@@ -5,8 +5,8 @@
 
 event bro_init()
 	{
-	local c1 = hll_cardinality_init(0.01);
-	local c2 = hll_cardinality_init(0.01);
+	local c1 = hll_cardinality_init(0.01, 0.95);
+	local c2 = hll_cardinality_init(0.01, 0.95);
 
 	local add1 = 2001;
 	local add2 = 2002;
@@ -46,7 +46,7 @@ event bro_init()
 	print "This value should be about 12:";
 	print hll_cardinality_estimate(c2);
 
-	local m2 = hll_cardinality_init(0.02);
+	local m2 = hll_cardinality_init(0.02, 0.95);
 
 	print "This value should be around 0:";
 	print hll_cardinality_estimate(m2);
@@ -56,7 +56,7 @@ event bro_init()
 	print "This value should be around 13:";
 	print hll_cardinality_estimate(c3);
 
-	c3 = hll_cardinality_init(0.01);
+	c3 = hll_cardinality_init(0.01, 0.95);
 	print "This value should be 0:";
 	print hll_cardinality_estimate(c3);
 
diff --git a/testing/btest/core/leaks/hll_cluster.bro b/testing/btest/core/leaks/hll_cluster.bro
index 0e342325c3..65fe8da447 100644
--- a/testing/btest/core/leaks/hll_cluster.bro
+++ b/testing/btest/core/leaks/hll_cluster.bro
@@ -36,7 +36,7 @@ global runnumber: count &redef; # differentiate runs
 
 event remote_connection_handshake_done(p: event_peer)
 	{
-	local c = hll_cardinality_init(0.01);
+	local c = hll_cardinality_init(0.01, 0.95);
 
 	local add1 = 2001;
 	local add2 = 2002;
@@ -92,7 +92,7 @@ global hll: opaque of cardinality;
 
 event bro_init()
 	{
-	hll = hll_cardinality_init(0.01);
+	hll = hll_cardinality_init(0.01, 0.95);
 	}
 
 event hll_data(data: opaque of cardinality)
diff --git a/testing/btest/istate/hll.bro b/testing/btest/istate/hll.bro
index 1dfca6c30f..511a892644 100644
--- a/testing/btest/istate/hll.bro
+++ b/testing/btest/istate/hll.bro
@@ -13,7 +13,7 @@ event bro_init()
 
 	if ( runnumber == 1 )
 		{
-		card = hll_cardinality_init(0.01);
+		card = hll_cardinality_init(0.01, 0.95);
 
 		hll_cardinality_add(card, "a");
 		hll_cardinality_add(card, "b");