diff --git a/DESCRIPTION b/DESCRIPTION
index 4c98cb4..b82219a 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -20,7 +20,6 @@ Imports:
     DelayedArray,
     DelayedMatrixStats,
     BiocParallel,
-    BiocNeighbors,
     stats,
     utils,
     Rcpp,
@@ -28,8 +27,7 @@ Imports:
 LinkingTo:
     Rcpp,
     beachmat,
-    assorthead (>= 1.3.5),
-    BiocNeighbors
+    assorthead (>= 1.3.5)
 Suggests:
     testthat,
     knitr,
diff --git a/NAMESPACE b/NAMESPACE
index 106ad47..107fdec 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -30,9 +30,6 @@ importClassesFrom(S4Vectors,DataFrame)
 importClassesFrom(S4Vectors,List)
 importClassesFrom(SummarizedExperiment,SummarizedExperiment)
 importFrom(BiocGenerics,cbind)
-importFrom(BiocNeighbors,AnnoyParam)
-importFrom(BiocNeighbors,KmknnParam)
-importFrom(BiocNeighbors,defineBuilder)
 importFrom(BiocParallel,SerialParam)
 importFrom(BiocParallel,bpnworkers)
 importFrom(DelayedArray,DelayedArray)
diff --git a/R/RcppExports.R b/R/RcppExports.R
index 56bd22a..dc6ac18 100644
--- a/R/RcppExports.R
+++ b/R/RcppExports.R
@@ -19,18 +19,14 @@ set_executor <- function(ptr) {
     .Call('_SingleR_set_executor', PACKAGE = 'SingleR', ptr)
 }
 
-train_integrated <- function(test_features, references, ref_features, labels, prebuilt, nthreads) {
-    .Call('_SingleR_train_integrated', PACKAGE = 'SingleR', test_features, references, ref_features, labels, prebuilt, nthreads)
+train_integrated <- function(test_nrow, test_features, references, ref_features, labels, prebuilt, nthreads) {
+    .Call('_SingleR_train_integrated', PACKAGE = 'SingleR', test_nrow, test_features, references, ref_features, labels, prebuilt, nthreads)
 }
 
 #' @importFrom Rcpp sourceCpp
 #' @useDynLib SingleR
-train_single <- function(test_features, ref, ref_features, labels, markers, builder, nthreads) {
-    .Call('_SingleR_train_single', PACKAGE = 'SingleR', test_features, ref, ref_features, labels, markers, builder, nthreads)
-}
-
-get_ref_subset <- function(built) {
-    .Call('_SingleR_get_ref_subset', PACKAGE = 'SingleR', built)
+train_single <- function(test_nrow, test_features, ref, ref_features, labels, markers, nthreads) {
+    .Call('_SingleR_train_single', PACKAGE = 'SingleR', test_nrow, test_features, ref, ref_features, labels, markers, nthreads)
 }
 
 is_valid_built <- function(built) {
diff --git a/R/combineRecomputedResults.R b/R/combineRecomputedResults.R
index adf3d93..3ddb026 100644
--- a/R/combineRecomputedResults.R
+++ b/R/combineRecomputedResults.R
@@ -163,6 +163,7 @@ combineRecomputedResults <- function(
 
     # Applying the integration.
     ibuilt <- train_integrated(
+        test_nrow=length(test.genes),
         test_features=all.inter.test,
         references=lapply(trained, function(x) initializeCpp(x$ref, .check.na=FALSE)),
         ref_features=all.inter.ref,
diff --git a/R/getClassicMarkers.R b/R/getClassicMarkers.R
index 4cf9b86..c00f1f4 100644
--- a/R/getClassicMarkers.R
+++ b/R/getClassicMarkers.R
@@ -71,7 +71,10 @@ getClassicMarkers <- function(ref, labels, assay.type="logcounts", check.missing
     }
     common <- as.character(common) # avoid problems with NULL rownames for zero-row inputs.
     for (i in seq_along(ref)) {
-        ref[[i]] <- DelayedArray(ref[[i]])[common,,drop=FALSE]
+        # Use match() as this works with zero-row matrices that aren't allowed to have rownames,
+        # see discussion at https://mailman.stat.ethz.ch/pipermail/r-devel/2006-August/038893.html.
+        curmat <- ref[[i]]
+        ref[[i]] <- DelayedArray(curmat)[match(common, rownames(curmat)),,drop=FALSE]
     }
 
     blocks <- NULL
diff --git a/R/rebuildIndices.R b/R/rebuildIndices.R
index 99185ee..cc62b77 100644
--- a/R/rebuildIndices.R
+++ b/R/rebuildIndices.R
@@ -46,9 +46,9 @@ rebuildIndex <- function(trained, num.threads=1) {
             markers=trained$markers$full, 
             labels=trained$labels$full, 
             ulabels=trained$labels$unique, 
-            BNPARAM=trained$options$BNPARAM,
             test.genes=trained$options$test.genes,
-            num.threads=num.threads) 
+            num.threads=num.threads
+        )$index
     }
     trained
 }
diff --git a/R/trainSingleR.R b/R/trainSingleR.R
index 345ce87..ad3f789 100644
--- a/R/trainSingleR.R
+++ b/R/trainSingleR.R
@@ -43,7 +43,7 @@
 #' if \code{ref} is a \link[SummarizedExperiment]{SummarizedExperiment} object (or is a list that contains one or more such objects).
 #' @param check.missing Logical scalar indicating whether rows should be checked for missing values.
 #' If true and any missing values are found, the rows containing these values are silently removed.
-#' @param BNPARAM A \link[BiocNeighbors]{BiocNeighborParam} object specifying how the neighbor search index should be constructed.
+#' @param BNPARAM Deprecated and ignored.
 #' @param approximate Deprecated, use \code{BNPARAM} instead.
 #' @param num.threads Integer scalar specifying the number of threads to use for index building.
 #' @param hint.sce Boolean indicating whether to print a hint to change \code{de.method=} when any entry of \code{ref} is a \link[SingleCellExperiment]{SingleCellExperiment}.
@@ -196,7 +196,6 @@
 #' 
 #' @export
 #' @importFrom S4Vectors List isSingleString metadata metadata<-
-#' @importFrom BiocNeighbors defineBuilder AnnoyParam KmknnParam
 #' @importFrom BiocParallel SerialParam
 #' @importFrom S4Vectors List
 #' @importFrom SummarizedExperiment assay
@@ -238,14 +237,6 @@ trainSingleR <- function(
         stop("list-like 'genes' should be the same length as 'ref'")
     }
 
-    if (is.null(BNPARAM)) {
-        if (approximate) {
-            BNPARAM <- AnnoyParam()
-        } else {
-            BNPARAM <- KmknnParam()
-        }
-    }
-
     output <- vector("list", length(ref))
     names(output) <- names(ref)
     for (l in seq_along(ref)) {
@@ -309,16 +300,15 @@ trainSingleR <- function(
             ulabels=ulabels,
             test.genes=test.genes,
             markers=markers,
-            BNPARAM=BNPARAM,
             num.threads=num.threads
         )
 
         output[[l]] <- List(
-            built = built,
+            built = built$index,
             ref = curref,
             labels = list(full = curlabels, unique = ulabels),
-            markers = list(full = markers, unique = rownames(curref)[get_ref_subset(built) + 1]),
-            options = list(BNPARAM = BNPARAM, test.genes = test.genes)
+            markers = list(full = markers, unique = rownames(curref)[built$ref_subset + 1]),
+            options = list(test.genes = test.genes)
         )
     }
 
@@ -370,7 +360,7 @@ trainSingleR <- function(
 }
 
 #' @importFrom beachmat initializeCpp
-.build_index <- function(ref, labels, ulabels, markers, test.genes, BNPARAM, num.threads) {
+.build_index <- function(ref, labels, ulabels, markers, test.genes, num.threads) {
     for (m in seq_along(markers)) {
         current <- markers[[m]]
         for (n in seq_along(current)) {
@@ -384,22 +374,23 @@ trainSingleR <- function(
     }
 
     if (is.null(test.genes)) {
+        test.nrow <- nrow(ref)
         test.genes <- ref.genes <- seq_len(nrow(ref))
     } else {
+        test.nrow <- length(test.genes)
         intersection <- .create_intersection(test.genes, rownames(ref))
         test.genes <- intersection$test
         ref.genes <- intersection$reference
     }
 
-    builder <- defineBuilder(BNPARAM)
     parsed <- initializeCpp(ref, .check.na=FALSE)
     train_single(
+        test_nrow=test.nrow,
         test_features=test.genes - 1L, 
         ref=parsed,
         ref_features=ref.genes - 1L,
         labels=match(labels, ulabels) - 1L,
         markers=markers,
-        builder=builder$builder,
         nthreads=num.threads
     )
 }
diff --git a/man/trainSingleR.Rd b/man/trainSingleR.Rd
index f9f7258..de59c1c 100644
--- a/man/trainSingleR.Rd
+++ b/man/trainSingleR.Rd
@@ -93,7 +93,7 @@ It will also suggest setting \code{aggr.ref=TRUE} for greater efficiency when \c
 
 \item{num.threads}{Integer scalar specifying the number of threads to use for index building.}
 
-\item{BNPARAM}{A \link[BiocNeighbors]{BiocNeighborParam} object specifying how the neighbor search index should be constructed.}
+\item{BNPARAM}{Deprecated and ignored.}
 
 \item{BPPARAM}{A \link[BiocParallel]{BiocParallelParam} object specifying how parallelization should be performed when \code{check.missing = TRUE}.}
 }
diff --git a/src/RcppExports.cpp b/src/RcppExports.cpp
index 932794c..37b20be 100644
--- a/src/RcppExports.cpp
+++ b/src/RcppExports.cpp
@@ -67,43 +67,34 @@ BEGIN_RCPP
 END_RCPP
 }
 // train_integrated
-SEXP train_integrated(Rcpp::List test_features, Rcpp::List references, Rcpp::List ref_features, Rcpp::List labels, Rcpp::List prebuilt, int nthreads);
-RcppExport SEXP _SingleR_train_integrated(SEXP test_featuresSEXP, SEXP referencesSEXP, SEXP ref_featuresSEXP, SEXP labelsSEXP, SEXP prebuiltSEXP, SEXP nthreadsSEXP) {
+SEXP train_integrated(int test_nrow, Rcpp::List test_features, Rcpp::List references, Rcpp::List ref_features, Rcpp::List labels, Rcpp::List prebuilt, int nthreads);
+RcppExport SEXP _SingleR_train_integrated(SEXP test_nrowSEXP, SEXP test_featuresSEXP, SEXP referencesSEXP, SEXP ref_featuresSEXP, SEXP labelsSEXP, SEXP prebuiltSEXP, SEXP nthreadsSEXP) {
 BEGIN_RCPP
     Rcpp::RObject rcpp_result_gen;
+    Rcpp::traits::input_parameter< int >::type test_nrow(test_nrowSEXP);
     Rcpp::traits::input_parameter< Rcpp::List >::type test_features(test_featuresSEXP);
     Rcpp::traits::input_parameter< Rcpp::List >::type references(referencesSEXP);
     Rcpp::traits::input_parameter< Rcpp::List >::type ref_features(ref_featuresSEXP);
     Rcpp::traits::input_parameter< Rcpp::List >::type labels(labelsSEXP);
     Rcpp::traits::input_parameter< Rcpp::List >::type prebuilt(prebuiltSEXP);
     Rcpp::traits::input_parameter< int >::type nthreads(nthreadsSEXP);
-    rcpp_result_gen = Rcpp::wrap(train_integrated(test_features, references, ref_features, labels, prebuilt, nthreads));
+    rcpp_result_gen = Rcpp::wrap(train_integrated(test_nrow, test_features, references, ref_features, labels, prebuilt, nthreads));
     return rcpp_result_gen;
 END_RCPP
 }
 // train_single
-SEXP train_single(Rcpp::IntegerVector test_features, Rcpp::RObject ref, Rcpp::IntegerVector ref_features, Rcpp::IntegerVector labels, Rcpp::List markers, Rcpp::RObject builder, int nthreads);
-RcppExport SEXP _SingleR_train_single(SEXP test_featuresSEXP, SEXP refSEXP, SEXP ref_featuresSEXP, SEXP labelsSEXP, SEXP markersSEXP, SEXP builderSEXP, SEXP nthreadsSEXP) {
+SEXP train_single(int test_nrow, Rcpp::IntegerVector test_features, Rcpp::RObject ref, Rcpp::IntegerVector ref_features, Rcpp::IntegerVector labels, Rcpp::List markers, int nthreads);
+RcppExport SEXP _SingleR_train_single(SEXP test_nrowSEXP, SEXP test_featuresSEXP, SEXP refSEXP, SEXP ref_featuresSEXP, SEXP labelsSEXP, SEXP markersSEXP, SEXP nthreadsSEXP) {
 BEGIN_RCPP
     Rcpp::RObject rcpp_result_gen;
+    Rcpp::traits::input_parameter< int >::type test_nrow(test_nrowSEXP);
     Rcpp::traits::input_parameter< Rcpp::IntegerVector >::type test_features(test_featuresSEXP);
     Rcpp::traits::input_parameter< Rcpp::RObject >::type ref(refSEXP);
     Rcpp::traits::input_parameter< Rcpp::IntegerVector >::type ref_features(ref_featuresSEXP);
     Rcpp::traits::input_parameter< Rcpp::IntegerVector >::type labels(labelsSEXP);
     Rcpp::traits::input_parameter< Rcpp::List >::type markers(markersSEXP);
-    Rcpp::traits::input_parameter< Rcpp::RObject >::type builder(builderSEXP);
     Rcpp::traits::input_parameter< int >::type nthreads(nthreadsSEXP);
-    rcpp_result_gen = Rcpp::wrap(train_single(test_features, ref, ref_features, labels, markers, builder, nthreads));
-    return rcpp_result_gen;
-END_RCPP
-}
-// get_ref_subset
-Rcpp::IntegerVector get_ref_subset(SEXP built);
-RcppExport SEXP _SingleR_get_ref_subset(SEXP builtSEXP) {
-BEGIN_RCPP
-    Rcpp::RObject rcpp_result_gen;
-    Rcpp::traits::input_parameter< SEXP >::type built(builtSEXP);
-    rcpp_result_gen = Rcpp::wrap(get_ref_subset(built));
+    rcpp_result_gen = Rcpp::wrap(train_single(test_nrow, test_features, ref, ref_features, labels, markers, nthreads));
     return rcpp_result_gen;
 END_RCPP
 }
@@ -123,9 +114,8 @@ static const R_CallMethodDef CallEntries[] = {
     {"_SingleR_classify_single", (DL_FUNC) &_SingleR_classify_single, 6},
     {"_SingleR_find_classic_markers", (DL_FUNC) &_SingleR_find_classic_markers, 6},
     {"_SingleR_set_executor", (DL_FUNC) &_SingleR_set_executor, 1},
-    {"_SingleR_train_integrated", (DL_FUNC) &_SingleR_train_integrated, 6},
+    {"_SingleR_train_integrated", (DL_FUNC) &_SingleR_train_integrated, 7},
     {"_SingleR_train_single", (DL_FUNC) &_SingleR_train_single, 7},
-    {"_SingleR_get_ref_subset", (DL_FUNC) &_SingleR_get_ref_subset, 1},
     {"_SingleR_is_valid_built", (DL_FUNC) &_SingleR_is_valid_built, 1},
     {NULL, NULL, 0}
 };
diff --git a/src/classify_single.cpp b/src/classify_single.cpp
index 56275c1..26d820e 100644
--- a/src/classify_single.cpp
+++ b/src/classify_single.cpp
@@ -7,7 +7,7 @@
 //[[Rcpp::export(rng=false)]]
 SEXP classify_single(Rcpp::RObject test, SEXP prebuilt, double quantile, bool use_fine_tune, double fine_tune_threshold, int nthreads) {
     Rtatami::BoundNumericPointer parsed(test);
-    TrainedSingleIntersectPointer built(prebuilt);
+    TrainedSinglePointer built(prebuilt);
 
     // Setting up outputs.
     size_t ncells = parsed->ptr->ncol();
@@ -34,7 +34,7 @@ SEXP classify_single(Rcpp::RObject test, SEXP prebuilt, double quantile, bool us
     opts.quantile = quantile;
     opts.fine_tune = use_fine_tune;
     opts.fine_tune_threshold = fine_tune_threshold;
-    singlepp::classify_single_intersect(*(parsed->ptr), *built, buffers, opts);
+    singlepp::classify_single(*(parsed->ptr), *built, buffers, opts);
 
     return Rcpp::List::create(
         Rcpp::Named("best") = best,
diff --git a/src/train_integrated.cpp b/src/train_integrated.cpp
index 259d9c5..8c5d949 100644
--- a/src/train_integrated.cpp
+++ b/src/train_integrated.cpp
@@ -4,7 +4,15 @@
 #include <memory>
 
 //[[Rcpp::export(rng=false)]]
-SEXP train_integrated(Rcpp::List test_features, Rcpp::List references, Rcpp::List ref_features, Rcpp::List labels, Rcpp::List prebuilt, int nthreads) {
+SEXP train_integrated(
+    int test_nrow,
+    Rcpp::List test_features,
+    Rcpp::List references,
+    Rcpp::List ref_features,
+    Rcpp::List labels,
+    Rcpp::List prebuilt,
+    int nthreads
+) {
     size_t nrefs = references.size();
 
     std::vector<singlepp::TrainIntegratedInput<double, int, int> > inputs;
@@ -29,9 +37,10 @@ SEXP train_integrated(Rcpp::List test_features, Rcpp::List references, Rcpp::Lis
 
         holding_labs[r] = labels[r];
         Rcpp::RObject built = prebuilt[r];
-        TrainedSingleIntersectPointer curbuilt(built);
+        TrainedSinglePointer curbuilt(built);
 
-        inputs.push_back(singlepp::prepare_integrated_input_intersect(
+        inputs.push_back(singlepp::prepare_integrated_input(
+            test_nrow,
             curinter,
             *(parsed->ptr),
             static_cast<const int*>(holding_labs[r].begin()), 
diff --git a/src/train_single.cpp b/src/train_single.cpp
index 4fba77f..f4441e9 100644
--- a/src/train_single.cpp
+++ b/src/train_single.cpp
@@ -1,5 +1,4 @@
 #include "utils.h" 
-#include "BiocNeighbors.h"
 
 #include <vector>
 #include <memory>
@@ -7,13 +6,18 @@
 //' @importFrom Rcpp sourceCpp
 //' @useDynLib SingleR
 //[[Rcpp::export(rng=false)]]
-SEXP train_single(Rcpp::IntegerVector test_features, Rcpp::RObject ref, Rcpp::IntegerVector ref_features, Rcpp::IntegerVector labels, Rcpp::List markers, Rcpp::RObject builder, int nthreads) {
+SEXP train_single(
+    int test_nrow, 
+    Rcpp::IntegerVector test_features,
+    Rcpp::RObject ref,
+    Rcpp::IntegerVector ref_features,
+    Rcpp::IntegerVector labels,
+    Rcpp::List markers,
+    int nthreads
+) {
+    // We use all available markers; assume subsetting was applied on the R side.
     singlepp::TrainSingleOptions opts;
     opts.num_threads = nthreads;
-    opts.top = -1; // Use all available markers; assume subsetting was applied on the R side.
-
-    BiocNeighbors::BuilderPointer bptr(builder);
-    opts.trainer = std::shared_ptr<BiocNeighbors::Builder>(std::shared_ptr<BiocNeighbors::Builder>{}, bptr.get()); // make a no-op shared pointer.
 
     Rtatami::BoundNumericPointer parsed(ref);
     int NR = parsed->ptr->nrow();
@@ -50,22 +54,21 @@ SEXP train_single(Rcpp::IntegerVector test_features, Rcpp::RObject ref, Rcpp::In
     }
 
     // Building the indices.
-    auto built = singlepp::train_single_intersect(
+    std::vector<int> ref_subset;
+    auto built = singlepp::train_single(
+        test_nrow,
         inter,
         *(parsed->ptr),
         static_cast<const int*>(labels.begin()),
         std::move(markers2),
+        &ref_subset,
         opts
     );
 
-    return TrainedSingleIntersectPointer(new TrainedSingleIntersect(std::move(built)), true);
-}
-
-//[[Rcpp::export(rng=false)]]
-Rcpp::IntegerVector get_ref_subset(SEXP built) {
-    TrainedSingleIntersectPointer ptr(built);
-    const auto& rsub = ptr->get_ref_subset();
-    return Rcpp::IntegerVector(rsub.begin(), rsub.end());
+    return Rcpp::List::create(
+        Rcpp::Named("index") = TrainedSinglePointer(new TrainedSingle(std::move(built)), true),
+        Rcpp::Named("ref_subset") = Rcpp::IntegerVector(ref_subset.begin(), ref_subset.end())
+    );
 }
 
 //[[Rcpp::export(rng=false)]]
diff --git a/src/utils.h b/src/utils.h
index 3e9f97e..ec40e2a 100644
--- a/src/utils.h
+++ b/src/utils.h
@@ -5,9 +5,9 @@
 #include "Rtatami.h" // before singlepp includes to ensure the tatami_r::parallelize() override is set.
 #include "singlepp/singlepp.hpp"
 
-typedef singlepp::TrainedSingleIntersect<int, double> TrainedSingleIntersect;
+typedef singlepp::TrainedSingle<int, double> TrainedSingle;
 
-typedef Rcpp::XPtr<TrainedSingleIntersect> TrainedSingleIntersectPointer;
+typedef Rcpp::XPtr<TrainedSingle> TrainedSinglePointer;
 
 typedef singlepp::TrainedIntegrated<int> TrainedIntegrated;