diff --git a/src/vdaf.rs b/src/vdaf.rs
index 8ea17b71..b53a6f58 100644
--- a/src/vdaf.rs
+++ b/src/vdaf.rs
@@ -303,7 +303,16 @@ pub trait Aggregator<const VERIFY_KEY_SIZE: usize, const NONCE_SIZE: usize>: Vda
         &self,
         agg_param: &Self::AggregationParam,
         output_shares: M,
-    ) -> Result<Self::AggregateShare, VdafError>;
+    ) -> Result<Self::AggregateShare, VdafError> {
+        let mut share = self.aggregate_init(agg_param);
+        for output_share in output_shares {
+            share.accumulate(&output_share)?;
+        }
+        Ok(share)
+    }
+
+    /// Create an empty aggregate share.
+    fn aggregate_init(&self, agg_param: &Self::AggregationParam) -> Self::AggregateShare;
 
     /// Validates an aggregation parameter with respect to all previous aggregaiton parameters used
     /// for the same input share. `prev` MUST be sorted from least to most recently used.
diff --git a/src/vdaf/dummy.rs b/src/vdaf/dummy.rs
index 1a78e3ee..9fec3a68 100644
--- a/src/vdaf/dummy.rs
+++ b/src/vdaf/dummy.rs
@@ -158,16 +158,8 @@ impl vdaf::Aggregator<0, 16> for Vdaf {
         (self.prep_step_fn)(&state)
     }
 
-    fn aggregate<M: IntoIterator<Item = Self::OutputShare>>(
-        &self,
-        _aggregation_param: &Self::AggregationParam,
-        output_shares: M,
-    ) -> Result<Self::AggregateShare, VdafError> {
-        let mut aggregate_share = AggregateShare(0);
-        for output_share in output_shares {
-            aggregate_share.accumulate(&output_share)?;
-        }
-        Ok(aggregate_share)
+    fn aggregate_init(&self, _agg_param: &Self::AggregationParam) -> Self::AggregateShare {
+        AggregateShare(0)
     }
 
     fn is_agg_param_valid(_cur: &Self::AggregationParam, _prev: &[Self::AggregationParam]) -> bool {
diff --git a/src/vdaf/mastic.rs b/src/vdaf/mastic.rs
index d16fbb09..15924165 100644
--- a/src/vdaf/mastic.rs
+++ b/src/vdaf/mastic.rs
@@ -725,23 +725,15 @@ where
         Ok(PrepareTransition::Finish(output_shares))
     }
 
-    fn aggregate<M: IntoIterator<Item = MasticOutputShare<T::Field>>>(
-        &self,
-        agg_param: &MasticAggregationParam,
-        output_shares: M,
-    ) -> Result<MasticAggregateShare<T::Field>, VdafError> {
-        let mut agg_share = MasticAggregateShare::<T::Field>::from(vec![
+    fn aggregate_init(&self, agg_param: &Self::AggregationParam) -> Self::AggregateShare {
+        MasticAggregateShare::<T::Field>::from(vec![
             T::Field::zero();
             self.vidpf.weight_parameter
                 * agg_param
                     .level_and_prefixes
                     .prefixes()
                     .len()
-        ]);
-        for output_share in output_shares.into_iter() {
-            agg_share.accumulate(&output_share)?;
-        }
-        Ok(agg_share)
+        ])
     }
 }
 
diff --git a/src/vdaf/poplar1.rs b/src/vdaf/poplar1.rs
index 5a54eabd..49d36654 100644
--- a/src/vdaf/poplar1.rs
+++ b/src/vdaf/poplar1.rs
@@ -1251,15 +1251,10 @@ impl<P: Xof<SEED_SIZE>, const SEED_SIZE: usize> Aggregator<SEED_SIZE, 16>
         }
     }
 
-    fn aggregate<M: IntoIterator<Item = Poplar1FieldVec>>(
-        &self,
-        agg_param: &Poplar1AggregationParam,
-        output_shares: M,
-    ) -> Result<Poplar1FieldVec, VdafError> {
-        aggregate(
+    fn aggregate_init(&self, agg_param: &Self::AggregationParam) -> Self::AggregateShare {
+        Poplar1FieldVec::zero(
             usize::from(agg_param.level) == self.bits - 1,
             agg_param.prefixes.len(),
-            output_shares,
         )
     }
 
diff --git a/src/vdaf/prio2.rs b/src/vdaf/prio2.rs
index 96a8f5a3..dd35e1e3 100644
--- a/src/vdaf/prio2.rs
+++ b/src/vdaf/prio2.rs
@@ -317,17 +317,8 @@ impl Aggregator<32, 16> for Prio2 {
         Ok(PrepareTransition::Finish(OutputShare::from(data)))
     }
 
-    fn aggregate<M: IntoIterator<Item = OutputShare<FieldPrio2>>>(
-        &self,
-        _agg_param: &Self::AggregationParam,
-        out_shares: M,
-    ) -> Result<AggregateShare<FieldPrio2>, VdafError> {
-        let mut agg_share = AggregateShare(vec![FieldPrio2::zero(); self.input_len]);
-        for out_share in out_shares.into_iter() {
-            agg_share.accumulate(&out_share)?;
-        }
-
-        Ok(agg_share)
+    fn aggregate_init(&self, _agg_param: &Self::AggregationParam) -> Self::AggregateShare {
+        AggregateShare(vec![FieldPrio2::zero(); self.input_len])
     }
 
     /// Returns `true` iff `prev.is_empty()`
diff --git a/src/vdaf/prio3.rs b/src/vdaf/prio3.rs
index 22250203..7ac8233b 100644
--- a/src/vdaf/prio3.rs
+++ b/src/vdaf/prio3.rs
@@ -1573,18 +1573,8 @@ where
         Ok(PrepareTransition::Finish(output_share))
     }
 
-    /// Aggregates a sequence of output shares into an aggregate share.
-    fn aggregate<It: IntoIterator<Item = OutputShare<T::Field>>>(
-        &self,
-        _agg_param: &(),
-        output_shares: It,
-    ) -> Result<AggregateShare<T::Field>, VdafError> {
-        let mut agg_share = AggregateShare(vec![T::Field::zero(); self.typ.output_len()]);
-        for output_share in output_shares.into_iter() {
-            agg_share.accumulate(&output_share)?;
-        }
-
-        Ok(agg_share)
+    fn aggregate_init(&self, _agg_param: &Self::AggregationParam) -> Self::AggregateShare {
+        AggregateShare(vec![T::Field::zero(); self.typ.output_len()])
     }
 
     /// Returns `true` iff `prev.is_empty()`