diff --git a/NEWS.md b/NEWS.md
index af7699b8..bf8bb9da 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,6 +1,7 @@
 # TreeDist 2.8.0.9000 (development)
 
-- `SpectralEigens()` survives values of nEig larger than the input
+- `SpectralEigens()` returns correct eigenvalues (smallest was overlooked)
+- `SpectralEigens()` handles values of nEig larger than the input
 
 # TreeDist 2.8.0 (2024-07-25)
 
diff --git a/R/spectral_clustering.R b/R/spectral_clustering.R
index 5a2a800d..cb85e911 100644
--- a/R/spectral_clustering.R
+++ b/R/spectral_clustering.R
@@ -24,6 +24,9 @@
 #' @family tree space functions
 #' @export
 SpectralEigens <- function(D, nn = 10L, nEig = 2L) {
+  if (nEig < 1) {
+    stop("nEig must be positive")
+  }
   
   MutualKnnGraph <- function(D, nn) {
     D <- as.matrix(D)
@@ -32,13 +35,13 @@ SpectralEigens <- function(D, nn = 10L, nEig = 2L) {
     # intialize the knn matrix
     knn_mat <- matrix(FALSE, nrow = dims[[1]], ncol = dims[[2]])
     
-    # find the 10 nearest neighbors for each point
+    # find the 10 nearest neighbours for each point
     for (i in seq_len(nrow(D))) {
       neighbor_index <- order(D[i, ])[2:(nn + 1)]
       knn_mat[i, ][neighbor_index] <- TRUE
     }
     
-    # Now we note that i,j are neighbors iff K[i,j] = 1 or K[j,i] = 1
+    # Now we note that i,j are neighbours iff K[i,j] = 1 or K[j, i] = 1
     knn_mat <- knn_mat | t(knn_mat) # find mutual knn
     
     # Return:
@@ -64,7 +67,7 @@ SpectralEigens <- function(D, nn = 10L, nEig = 2L) {
   
   if (nL > nEig) {
     # Return the eigenvectors of the n_eig smallest eigenvalues:
-    ei[["vectors"]][, nL - rev(seq_len(nEig))]
+    ei[["vectors"]][, nL - (0:(nEig - 1))]
   } else {
     ei[["vectors"]]
   }
diff --git a/tests/testthat/test-spectral_clustering.R b/tests/testthat/test-spectral_clustering.R
new file mode 100644
index 00000000..5d3952bf
--- /dev/null
+++ b/tests/testthat/test-spectral_clustering.R
@@ -0,0 +1,11 @@
+d <- dist(c(1:20, 60:41))
+
+test_that("Spectral clustering fails gracefully", {
+  expect_error(SpectralEigens(d, nEig = 0), "nEig must be.*positive")
+})
+
+test_that("Spectral clustering works", {
+  allEig <- SpectralEigens(d, nEig = Inf)
+  expect_equal(dim(allEig), c(40, 40))
+  expect_equal(SpectralEigens(d, nEig = 2), allEig[, 40:39])
+})