diff --git a/ecc/bls12-377/fr/fft/domain.go b/ecc/bls12-377/fr/fft/domain.go
index 3ad436c4f7..ad939c6177 100644
--- a/ecc/bls12-377/fr/fft/domain.go
+++ b/ecc/bls12-377/fr/fft/domain.go
@@ -188,7 +188,7 @@ func (d *Domain) preComputeTwiddles() {
 		cosetGensInv[0].Set(&d.FinerGeneratorInv)
 		for i := 1; i < nbCosets; i++ {
 			cosetGens[i].Mul(&cosetGens[i-1], &d.FinerGenerator)
-			cosetGensInv[i].Mul(&cosetGensInv[1], &d.FinerGeneratorInv)
+			cosetGensInv[i].Mul(&cosetGensInv[i-1], &d.FinerGeneratorInv)
 		}
 		wg.Add(2 + 2*nbCosets)
 		go twiddles(d.Twiddles, d.Generator)
@@ -246,9 +246,13 @@ func precomputeExpTable(w fr.Element, table []fr.Element) {
 }
 
 func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
-	table[0].Exp(w, new(big.Int).SetUint64(power))
-	for i := 1; i < len(table); i++ {
-		table[i].Mul(&table[i-1], &w)
+
+	// this condition ensures that creating a domain of size 1 with cosets don't fail
+	if len(table) > 0 {
+		table[0].Exp(w, new(big.Int).SetUint64(power))
+		for i := 1; i < len(table); i++ {
+			table[i].Mul(&table[i-1], &w)
+		}
 	}
 }
 
diff --git a/ecc/bls12-377/fr/fft/fft_test.go b/ecc/bls12-377/fr/fft/fft_test.go
index 9471742b0c..ebd66639b7 100644
--- a/ecc/bls12-377/fr/fft/fft_test.go
+++ b/ecc/bls12-377/fr/fft/fft_test.go
@@ -31,8 +31,9 @@ import (
 func TestFFT(t *testing.T) {
 	const maxSize = 1 << 10
 
-	domainWithPrecompute := NewDomain(maxSize, 1, true)
-	domainWOPrecompute := NewDomain(maxSize, 1, false)
+	nbCosets := 3
+	domainWithPrecompute := NewDomain(maxSize, 2, true)
+	domainWOPrecompute := NewDomain(maxSize, 2, false)
 
 	parameters := gopter.DefaultTestParameters()
 	parameters.MinSuccessfulTests = 5
@@ -186,15 +187,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWithPrecompute.FFT(pol, DIT, 1)
-			domainWithPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWithPrecompute.FFT(pol, DIT, uint64(i))
+				domainWithPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
@@ -211,15 +217,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWOPrecompute.FFT(pol, DIT, 1)
-			domainWOPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWOPrecompute.FFT(pol, DIT, uint64(i))
+				domainWOPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
diff --git a/ecc/bls12-381/fr/fft/domain.go b/ecc/bls12-381/fr/fft/domain.go
index 654648a9e6..af43749ec3 100644
--- a/ecc/bls12-381/fr/fft/domain.go
+++ b/ecc/bls12-381/fr/fft/domain.go
@@ -188,7 +188,7 @@ func (d *Domain) preComputeTwiddles() {
 		cosetGensInv[0].Set(&d.FinerGeneratorInv)
 		for i := 1; i < nbCosets; i++ {
 			cosetGens[i].Mul(&cosetGens[i-1], &d.FinerGenerator)
-			cosetGensInv[i].Mul(&cosetGensInv[1], &d.FinerGeneratorInv)
+			cosetGensInv[i].Mul(&cosetGensInv[i-1], &d.FinerGeneratorInv)
 		}
 		wg.Add(2 + 2*nbCosets)
 		go twiddles(d.Twiddles, d.Generator)
@@ -246,9 +246,13 @@ func precomputeExpTable(w fr.Element, table []fr.Element) {
 }
 
 func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
-	table[0].Exp(w, new(big.Int).SetUint64(power))
-	for i := 1; i < len(table); i++ {
-		table[i].Mul(&table[i-1], &w)
+
+	// this condition ensures that creating a domain of size 1 with cosets don't fail
+	if len(table) > 0 {
+		table[0].Exp(w, new(big.Int).SetUint64(power))
+		for i := 1; i < len(table); i++ {
+			table[i].Mul(&table[i-1], &w)
+		}
 	}
 }
 
diff --git a/ecc/bls12-381/fr/fft/fft_test.go b/ecc/bls12-381/fr/fft/fft_test.go
index d610e5829b..0ed6c74041 100644
--- a/ecc/bls12-381/fr/fft/fft_test.go
+++ b/ecc/bls12-381/fr/fft/fft_test.go
@@ -31,8 +31,9 @@ import (
 func TestFFT(t *testing.T) {
 	const maxSize = 1 << 10
 
-	domainWithPrecompute := NewDomain(maxSize, 1, true)
-	domainWOPrecompute := NewDomain(maxSize, 1, false)
+	nbCosets := 3
+	domainWithPrecompute := NewDomain(maxSize, 2, true)
+	domainWOPrecompute := NewDomain(maxSize, 2, false)
 
 	parameters := gopter.DefaultTestParameters()
 	parameters.MinSuccessfulTests = 5
@@ -186,15 +187,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWithPrecompute.FFT(pol, DIT, 1)
-			domainWithPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWithPrecompute.FFT(pol, DIT, uint64(i))
+				domainWithPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
@@ -211,15 +217,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWOPrecompute.FFT(pol, DIT, 1)
-			domainWOPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWOPrecompute.FFT(pol, DIT, uint64(i))
+				domainWOPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
diff --git a/ecc/bn254/fr/fft/domain.go b/ecc/bn254/fr/fft/domain.go
index 18e8351d1f..a842c30bbc 100644
--- a/ecc/bn254/fr/fft/domain.go
+++ b/ecc/bn254/fr/fft/domain.go
@@ -188,7 +188,7 @@ func (d *Domain) preComputeTwiddles() {
 		cosetGensInv[0].Set(&d.FinerGeneratorInv)
 		for i := 1; i < nbCosets; i++ {
 			cosetGens[i].Mul(&cosetGens[i-1], &d.FinerGenerator)
-			cosetGensInv[i].Mul(&cosetGensInv[1], &d.FinerGeneratorInv)
+			cosetGensInv[i].Mul(&cosetGensInv[i-1], &d.FinerGeneratorInv)
 		}
 		wg.Add(2 + 2*nbCosets)
 		go twiddles(d.Twiddles, d.Generator)
@@ -246,9 +246,13 @@ func precomputeExpTable(w fr.Element, table []fr.Element) {
 }
 
 func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
-	table[0].Exp(w, new(big.Int).SetUint64(power))
-	for i := 1; i < len(table); i++ {
-		table[i].Mul(&table[i-1], &w)
+
+	// this condition ensures that creating a domain of size 1 with cosets don't fail
+	if len(table) > 0 {
+		table[0].Exp(w, new(big.Int).SetUint64(power))
+		for i := 1; i < len(table); i++ {
+			table[i].Mul(&table[i-1], &w)
+		}
 	}
 }
 
diff --git a/ecc/bn254/fr/fft/fft_test.go b/ecc/bn254/fr/fft/fft_test.go
index e934fc202d..57ffb6081f 100644
--- a/ecc/bn254/fr/fft/fft_test.go
+++ b/ecc/bn254/fr/fft/fft_test.go
@@ -31,8 +31,9 @@ import (
 func TestFFT(t *testing.T) {
 	const maxSize = 1 << 10
 
-	domainWithPrecompute := NewDomain(maxSize, 1, true)
-	domainWOPrecompute := NewDomain(maxSize, 1, false)
+	nbCosets := 3
+	domainWithPrecompute := NewDomain(maxSize, 2, true)
+	domainWOPrecompute := NewDomain(maxSize, 2, false)
 
 	parameters := gopter.DefaultTestParameters()
 	parameters.MinSuccessfulTests = 5
@@ -186,15 +187,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWithPrecompute.FFT(pol, DIT, 1)
-			domainWithPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWithPrecompute.FFT(pol, DIT, uint64(i))
+				domainWithPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
@@ -211,15 +217,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWOPrecompute.FFT(pol, DIT, 1)
-			domainWOPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWOPrecompute.FFT(pol, DIT, uint64(i))
+				domainWOPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
diff --git a/ecc/bw6-761/fr/fft/domain.go b/ecc/bw6-761/fr/fft/domain.go
index 3d025b1703..42f3ebead7 100644
--- a/ecc/bw6-761/fr/fft/domain.go
+++ b/ecc/bw6-761/fr/fft/domain.go
@@ -188,7 +188,7 @@ func (d *Domain) preComputeTwiddles() {
 		cosetGensInv[0].Set(&d.FinerGeneratorInv)
 		for i := 1; i < nbCosets; i++ {
 			cosetGens[i].Mul(&cosetGens[i-1], &d.FinerGenerator)
-			cosetGensInv[i].Mul(&cosetGensInv[1], &d.FinerGeneratorInv)
+			cosetGensInv[i].Mul(&cosetGensInv[i-1], &d.FinerGeneratorInv)
 		}
 		wg.Add(2 + 2*nbCosets)
 		go twiddles(d.Twiddles, d.Generator)
@@ -246,9 +246,13 @@ func precomputeExpTable(w fr.Element, table []fr.Element) {
 }
 
 func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
-	table[0].Exp(w, new(big.Int).SetUint64(power))
-	for i := 1; i < len(table); i++ {
-		table[i].Mul(&table[i-1], &w)
+
+	// this condition ensures that creating a domain of size 1 with cosets don't fail
+	if len(table) > 0 {
+		table[0].Exp(w, new(big.Int).SetUint64(power))
+		for i := 1; i < len(table); i++ {
+			table[i].Mul(&table[i-1], &w)
+		}
 	}
 }
 
diff --git a/ecc/bw6-761/fr/fft/fft_test.go b/ecc/bw6-761/fr/fft/fft_test.go
index aa44030b2f..40d5e52620 100644
--- a/ecc/bw6-761/fr/fft/fft_test.go
+++ b/ecc/bw6-761/fr/fft/fft_test.go
@@ -31,8 +31,9 @@ import (
 func TestFFT(t *testing.T) {
 	const maxSize = 1 << 10
 
-	domainWithPrecompute := NewDomain(maxSize, 1, true)
-	domainWOPrecompute := NewDomain(maxSize, 1, false)
+	nbCosets := 3
+	domainWithPrecompute := NewDomain(maxSize, 2, true)
+	domainWOPrecompute := NewDomain(maxSize, 2, false)
 
 	parameters := gopter.DefaultTestParameters()
 	parameters.MinSuccessfulTests = 5
@@ -186,15 +187,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWithPrecompute.FFT(pol, DIT, 1)
-			domainWithPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWithPrecompute.FFT(pol, DIT, uint64(i))
+				domainWithPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
@@ -211,15 +217,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWOPrecompute.FFT(pol, DIT, 1)
-			domainWOPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWOPrecompute.FFT(pol, DIT, uint64(i))
+				domainWOPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
diff --git a/internal/generator/fft/template/domain.go.tmpl b/internal/generator/fft/template/domain.go.tmpl
index f8b79d4c03..bfbf58d5b6 100644
--- a/internal/generator/fft/template/domain.go.tmpl
+++ b/internal/generator/fft/template/domain.go.tmpl
@@ -179,7 +179,7 @@ func (d *Domain) preComputeTwiddles() {
 		cosetGensInv[0].Set(&d.FinerGeneratorInv)
 		for i := 1; i < nbCosets; i++ {
 			cosetGens[i].Mul(&cosetGens[i-1], &d.FinerGenerator)
-			cosetGensInv[i].Mul(&cosetGensInv[1], &d.FinerGeneratorInv)
+			cosetGensInv[i].Mul(&cosetGensInv[i-1], &d.FinerGeneratorInv)
 		}
 		wg.Add(2 + 2*nbCosets)
 		go twiddles(d.Twiddles, d.Generator)
@@ -237,9 +237,13 @@ func precomputeExpTable(w fr.Element, table []fr.Element) {
 }
 
 func precomputeExpTableChunk(w fr.Element, power uint64, table []fr.Element) {
-	table[0].Exp(w, new(big.Int).SetUint64(power))
-	for i := 1; i < len(table); i++ {
-		table[i].Mul(&table[i-1], &w)
+	
+	// this condition ensures that creating a domain of size 1 with cosets don't fail
+	if len(table) > 0 {
+		table[0].Exp(w, new(big.Int).SetUint64(power))
+		for i := 1; i < len(table); i++ {
+			table[i].Mul(&table[i-1], &w)
+		}
 	}
 }
 
diff --git a/internal/generator/fft/template/tests/fft.go.tmpl b/internal/generator/fft/template/tests/fft.go.tmpl
index 754b133dd1..26e5666308 100644
--- a/internal/generator/fft/template/tests/fft.go.tmpl
+++ b/internal/generator/fft/template/tests/fft.go.tmpl
@@ -14,8 +14,9 @@ import (
 func TestFFT(t *testing.T) {
 	const maxSize = 1 << 10
 
-	domainWithPrecompute := NewDomain(maxSize, 1, true)
-	domainWOPrecompute := NewDomain(maxSize, 1, false)
+	nbCosets := 3
+	domainWithPrecompute := NewDomain(maxSize, 2, true)
+	domainWOPrecompute := NewDomain(maxSize, 2, false)
 
 	parameters := gopter.DefaultTestParameters()
 	parameters.MinSuccessfulTests = 5
@@ -169,15 +170,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWithPrecompute.FFT(pol, DIT, 1)
-			domainWithPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWithPrecompute.FFT(pol, DIT, uint64(i))
+				domainWithPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))
@@ -194,15 +200,20 @@ func TestFFT(t *testing.T) {
 			}
 			copy(backupPol, pol)
 
-			BitReverse(pol)
-			domainWOPrecompute.FFT(pol, DIT, 1)
-			domainWOPrecompute.FFTInverse(pol, DIF, 1)
-			BitReverse(pol)
-
 			check := true
-			for i := 0; i < len(pol); i++ {
-				check = check && pol[i].Equal(&backupPol[i])
+
+			for i := 1; i <= nbCosets; i++ {
+
+				BitReverse(pol)
+				domainWOPrecompute.FFT(pol, DIT, uint64(i))
+				domainWOPrecompute.FFTInverse(pol, DIF, uint64(i))
+				BitReverse(pol)
+
+				for i := 0; i < len(pol); i++ {
+					check = check && pol[i].Equal(&backupPol[i])
+				}
 			}
+
 			return check
 		},
 	))