diff --git a/src/bin/bench_recursion.rs b/src/bin/bench_recursion.rs
index 4a535d20..3b71c6f4 100644
--- a/src/bin/bench_recursion.rs
+++ b/src/bin/bench_recursion.rs
@@ -34,7 +34,7 @@ fn bench_prove<F: Field + Extendable<D>, const D: usize>() -> Result<()> {
         },
     };
 
-    let inputs = PartialWitness::new(1 << 14, config.num_wires, 1000);
+    let inputs = PartialWitness::new(config.num_wires);
     let mut builder = CircuitBuilder::<F, D>::new(config);
 
     let zero = builder.zero();
diff --git a/src/gadgets/arithmetic_extension.rs b/src/gadgets/arithmetic_extension.rs
index 15f1de9b..29b759fb 100644
--- a/src/gadgets/arithmetic_extension.rs
+++ b/src/gadgets/arithmetic_extension.rs
@@ -603,7 +603,7 @@ mod tests {
 
         let config = CircuitConfig::large_config();
 
-        let mut pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let mut pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, D>::new(config);
 
         let vs = FF::rand_vec(3);
@@ -640,7 +640,7 @@ mod tests {
 
         let config = CircuitConfig::large_config();
 
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, D>::new(config);
 
         let x = FF::rand();
diff --git a/src/gadgets/insert.rs b/src/gadgets/insert.rs
index bc91a013..bdc8bde7 100644
--- a/src/gadgets/insert.rs
+++ b/src/gadgets/insert.rs
@@ -64,7 +64,7 @@ mod tests {
         type FF = QuarticCrandallField;
         let len = 1 << len_log;
         let config = CircuitConfig::large_config();
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config);
         let v = (0..len - 1)
             .map(|_| builder.constant_extension(FF::rand()))
diff --git a/src/gadgets/interpolation.rs b/src/gadgets/interpolation.rs
index bba3befe..8ed5346a 100644
--- a/src/gadgets/interpolation.rs
+++ b/src/gadgets/interpolation.rs
@@ -70,7 +70,7 @@ mod tests {
         type F = CrandallField;
         type FF = QuarticCrandallField;
         let config = CircuitConfig::large_config();
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config);
 
         let len = 4;
@@ -110,7 +110,7 @@ mod tests {
         type F = CrandallField;
         type FF = QuarticCrandallField;
         let config = CircuitConfig::large_config();
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config);
 
         let len = 2;
diff --git a/src/gadgets/random_access.rs b/src/gadgets/random_access.rs
index 36b15e5b..395d920e 100644
--- a/src/gadgets/random_access.rs
+++ b/src/gadgets/random_access.rs
@@ -50,7 +50,7 @@ mod tests {
         type FF = QuarticCrandallField;
         let len = 1 << len_log;
         let config = CircuitConfig::large_config();
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config);
         let vec = FF::rand_vec(len);
         let v: Vec<_> = vec.iter().map(|x| builder.constant_extension(*x)).collect();
diff --git a/src/gadgets/select.rs b/src/gadgets/select.rs
index ce9eed58..58de09c6 100644
--- a/src/gadgets/select.rs
+++ b/src/gadgets/select.rs
@@ -48,7 +48,7 @@ mod tests {
         type F = CrandallField;
         type FF = QuarticCrandallField;
         let config = CircuitConfig::large_config();
-        let mut pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let mut pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config);
 
         let (x, y) = (FF::rand(), FF::rand());
diff --git a/src/gadgets/split_base.rs b/src/gadgets/split_base.rs
index af67d99c..ff420ba0 100644
--- a/src/gadgets/split_base.rs
+++ b/src/gadgets/split_base.rs
@@ -99,7 +99,7 @@ mod tests {
     fn test_split_base() -> Result<()> {
         type F = CrandallField;
         let config = CircuitConfig::large_config();
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config);
         let x = F::from_canonical_usize(0b110100000); // 416 = 1532 in base 6.
         let xt = builder.constant(x);
@@ -125,7 +125,7 @@ mod tests {
     fn test_base_sum() -> Result<()> {
         type F = CrandallField;
         let config = CircuitConfig::large_config();
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config);
 
         let n = thread_rng().gen_range(0, 1 << 10);
diff --git a/src/gates/gate_testing.rs b/src/gates/gate_testing.rs
index 00632d49..66bed775 100644
--- a/src/gates/gate_testing.rs
+++ b/src/gates/gate_testing.rs
@@ -124,7 +124,7 @@ pub(crate) fn test_eval_fns<F: Extendable<D>, G: Gate<F, D>, const D: usize>(
     let constants = F::Extension::rand_vec(gate.num_constants());
 
     let config = CircuitConfig::large_config();
-    let mut pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+    let mut pw = PartialWitness::new(config.num_wires);
     let mut builder = CircuitBuilder::<F, D>::new(config);
 
     let wires_t = builder.add_virtual_extension_targets(wires.len());
diff --git a/src/gates/gmimc.rs b/src/gates/gmimc.rs
index 46c7b975..03fdef56 100644
--- a/src/gates/gmimc.rs
+++ b/src/gates/gmimc.rs
@@ -345,7 +345,7 @@ mod tests {
 
         let permutation_inputs = (0..W).map(F::from_canonical_usize).collect::<Vec<_>>();
 
-        let mut witness = PartialWitness::new(1 << 14, 126, 1000);
+        let mut witness = PartialWitness::new(126);
         witness.set_wire(
             Wire {
                 gate: 0,
diff --git a/src/hash/merkle_proofs.rs b/src/hash/merkle_proofs.rs
index 139ab0bc..088ffc5a 100644
--- a/src/hash/merkle_proofs.rs
+++ b/src/hash/merkle_proofs.rs
@@ -154,7 +154,7 @@ mod tests {
     fn test_recursive_merkle_proof() -> Result<()> {
         type F = CrandallField;
         let config = CircuitConfig::large_config();
-        let mut pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let mut pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config);
 
         let log_n = 8;
diff --git a/src/iop/challenger.rs b/src/iop/challenger.rs
index 4c13692f..1e41ecea 100644
--- a/src/iop/challenger.rs
+++ b/src/iop/challenger.rs
@@ -399,7 +399,7 @@ mod tests {
             num_routed_wires: 27,
             ..CircuitConfig::default()
         };
-        let mut witness = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let mut witness = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, 4>::new(config.clone());
         let mut recursive_challenger = RecursiveChallenger::new(&mut builder);
         let mut recursive_outputs_per_round: Vec<Vec<Target>> = Vec::new();
diff --git a/src/iop/witness.rs b/src/iop/witness.rs
index 1eabad4b..da7ee73f 100644
--- a/src/iop/witness.rs
+++ b/src/iop/witness.rs
@@ -31,10 +31,10 @@ pub struct PartialWitness<F: Field> {
 }
 
 impl<F: Field> PartialWitness<F> {
-    pub fn new(degree: usize, num_wires: usize, max_virtual_target: usize) -> Self {
+    pub fn new(num_wires: usize) -> Self {
         PartialWitness {
-            wire_values: vec![vec![None; num_wires]; degree],
-            virtual_target_values: vec![None; max_virtual_target],
+            wire_values: vec![vec![None; num_wires]],
+            virtual_target_values: vec![],
         }
     }
 
@@ -93,8 +93,13 @@ impl<F: Field> PartialWitness<F> {
 
     pub fn contains(&self, target: Target) -> bool {
         match target {
-            Target::Wire(Wire { gate, input }) => self.wire_values[gate][input].is_some(),
-            Target::VirtualTarget { index } => self.virtual_target_values[index].is_some(),
+            Target::Wire(Wire { gate, input }) => {
+                self.wire_values.len() > gate && self.wire_values[gate][input].is_some()
+            }
+            Target::VirtualTarget { index } => {
+                self.virtual_target_values.len() > index
+                    && self.virtual_target_values[index].is_some()
+            }
         }
     }
 
@@ -105,6 +110,10 @@ impl<F: Field> PartialWitness<F> {
     pub fn set_target(&mut self, target: Target, value: F) {
         match target {
             Target::Wire(Wire { gate, input }) => {
+                if gate >= self.wire_values.len() {
+                    self.wire_values
+                        .resize(gate + 1, vec![None; self.wire_values[0].len()]);
+                }
                 if let Some(old_value) = self.wire_values[gate][input] {
                     assert_eq!(
                         old_value, value,
@@ -116,6 +125,9 @@ impl<F: Field> PartialWitness<F> {
                 }
             }
             Target::VirtualTarget { index } => {
+                if index >= self.virtual_target_values.len() {
+                    self.virtual_target_values.resize(index + 1, None);
+                }
                 if let Some(old_value) = self.virtual_target_values[index] {
                     assert_eq!(
                         old_value, value,
@@ -192,7 +204,7 @@ impl<F: Field> PartialWitness<F> {
 
     pub fn full_witness(self, degree: usize, num_wires: usize) -> Witness<F> {
         let mut wire_values = vec![vec![F::ZERO; degree]; num_wires];
-        for i in 0..degree {
+        for i in 0..self.wire_values.len().min(degree) {
             for j in 0..num_wires {
                 wire_values[j][i] = self.wire_values[i][j].unwrap_or(F::ZERO);
             }
@@ -237,9 +249,3 @@ impl<F: Field> PartialWitness<F> {
         Ok(())
     }
 }
-
-impl<F: Field> Default for PartialWitness<F> {
-    fn default() -> Self {
-        Self::new(0, 0, 0)
-    }
-}
diff --git a/src/plonk/recursive_verifier.rs b/src/plonk/recursive_verifier.rs
index 64175a20..ee5f82b9 100644
--- a/src/plonk/recursive_verifier.rs
+++ b/src/plonk/recursive_verifier.rs
@@ -383,7 +383,7 @@ mod tests {
             }
             let data = builder.build();
             (
-                data.prove(PartialWitness::new(1 << 14, config.num_wires, 1000))?,
+                data.prove(PartialWitness::new(config.num_wires))?,
                 data.verifier_only,
                 data.common,
             )
@@ -391,7 +391,7 @@ mod tests {
         verify(proof_with_pis.clone(), &vd, &cd)?;
 
         let mut builder = CircuitBuilder::<F, D>::new(config.clone());
-        let mut pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let mut pw = PartialWitness::new(config.num_wires);
         let pt = proof_to_proof_target(&proof_with_pis, &mut builder);
         set_proof_target(&proof_with_pis, &pt, &mut pw);
 
@@ -438,7 +438,7 @@ mod tests {
                 }
                 let data = builder.build();
                 (
-                    data.prove(PartialWitness::new(1 << 14, config.num_wires, 1000))?,
+                    data.prove(PartialWitness::new(config.num_wires))?,
                     data.verifier_only,
                     data.common,
                 )
@@ -446,7 +446,7 @@ mod tests {
             verify(proof_with_pis.clone(), &vd, &cd)?;
 
             let mut builder = CircuitBuilder::<F, D>::new(config.clone());
-            let mut pw = PartialWitness::new(1 << 14, config.num_wires, 100000);
+            let mut pw = PartialWitness::new(config.num_wires);
             let pt = proof_to_proof_target(&proof_with_pis, &mut builder);
             set_proof_target(&proof_with_pis, &pt, &mut pw);
 
@@ -464,7 +464,7 @@ mod tests {
 
         verify(proof_with_pis.clone(), &vd, &cd)?;
         let mut builder = CircuitBuilder::<F, D>::new(config.clone());
-        let mut pw = PartialWitness::new(1 << 14, config.num_wires, 100000);
+        let mut pw = PartialWitness::new(config.num_wires);
         let pt = proof_to_proof_target(&proof_with_pis, &mut builder);
         set_proof_target(&proof_with_pis, &pt, &mut pw);
 
diff --git a/src/util/reducing.rs b/src/util/reducing.rs
index 47386e75..ce6827ba 100644
--- a/src/util/reducing.rs
+++ b/src/util/reducing.rs
@@ -249,7 +249,7 @@ mod tests {
 
         let config = CircuitConfig::large_config();
 
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, D>::new(config);
 
         let alpha = FF::rand();
@@ -277,7 +277,7 @@ mod tests {
 
         let config = CircuitConfig::large_config();
 
-        let pw = PartialWitness::new(1 << 14, config.num_wires, 1000);
+        let pw = PartialWitness::new(config.num_wires);
         let mut builder = CircuitBuilder::<F, D>::new(config);
 
         let alpha = FF::rand();