diff --git a/include/utilities/threshold/basics.hpp b/include/utilities/threshold/basics.hpp
index d5602a41..99a3fdc7 100644
--- a/include/utilities/threshold/basics.hpp
+++ b/include/utilities/threshold/basics.hpp
@@ -30,10 +30,9 @@ double expected_kmer_occurrences(var_t const & bin_size,
 /**
  * @brief K-mer lemma threshold.
 */
-template <typename var_t>
-var_t kmer_lemma_threshold(size_t const l, var_t const k, var_t const e)
+inline size_t kmer_lemma_threshold(size_t const l, uint8_t const k, uint8_t const e)
 {
-    if (((int64_t) l - k + 1) <= (int64_t) e*k)
+    if ((l - k + 1) <= (size_t) e*k)
         return 0;
     
     return l - k + 1 - e * k;
diff --git a/include/utilities/threshold/filtering_request.hpp b/include/utilities/threshold/filtering_request.hpp
index 3fe2cc37..b079d439 100755
--- a/include/utilities/threshold/filtering_request.hpp
+++ b/include/utilities/threshold/filtering_request.hpp
@@ -6,6 +6,8 @@
 namespace valik
 {
 
+constexpr uint8_t query_every = 2; // query every 2nd pattern by default
+
 /**
  * @brief The user requests filtering by setting the following parameters.
  * 
@@ -90,21 +92,60 @@ struct filtering_request
         return std::max(0.0, fpr);
     }
 
+    /**
+     * @brief The probability of at least threshold k-mers matching spuriously between a query pattern and a reference bin.
+    */
+    double pattern_spurious_match_prob(param_set const & params, uint64_t const & ref_s, size_t const ref_b) const
+    {
+        double fpr{1};
+        //!TODO: expected k-mer occurrences and pattern spurious match probability should be independent of the current sequence being processed
+        double p = std::min(1.0, expected_kmer_occurrences(std::round(ref_s / (double) ref_b), params.k)); 
+        /*
+        For parameters 
+        
+        s reference size
+        b number of bins
+        k kmer size
+        l min match length
+        t threshold 
+
+        find the probability of t or more k-mers matching spuriously between a pattern of length l and a reference bin.   
+        
+        The probability of a pattern exceeding the threshold by chance is equal to 1 - P(0 k-mers match) - 
+                                                                                       P(1 k-mer matches) - 
+                                                                                       ... - 
+                                                                                       P(t - 1 k-mers match).
+
+        Given p which is the probability of a single k-mer appearing spuriously in the reference bin and n = (l - k + 1) k-mers per pattern 
+        the probability of 0 k-mers matching spuriously is P(0 k-mers match) = (1 - p)^n 
+        and
+        the probability of 1 k-mer out of n matching is P(1 k-mer matches) = (n take 1) * p^1 * (1 - p)^(n - 1).
+        */
+
+        size_t kmers_per_pattern = l - params.k + 1;
+        for (uint8_t matching_kmer_count{0}; matching_kmer_count < params.t; matching_kmer_count++)
+        {
+            fpr -= combinations(matching_kmer_count, kmers_per_pattern) * 
+                                pow(p, matching_kmer_count) * 
+                                pow(1 - p, kmers_per_pattern - matching_kmer_count);
+        }
+
+        return std::max(0.0, fpr);
+    }
+
     /**
      * @brief An approximation of the probability of a query segment having a spurious match in a reference bin. 
     */
-    double fpr(param_set const & params, uint64_t const & query_seg_len) const
+    double fpr(param_set const & params, uint64_t const & query_seg_len, uint64_t const & ref_size, size_t const ref_bins) const
     {
-        double pattern_p = pattern_spurious_match_prob(params);
+        double pattern_p = pattern_spurious_match_prob(params, ref_size, ref_bins);
         /*
         uint64_t independent_patterns_per_segment = query_seg_len / (double) l;
         double independent_patterns_p = std::min(1.0, pattern_p * independent_patterns_per_segment);
         std::cout << "independent_patterns_p\t" << independent_patterns_p << '\n';
         */
-        constexpr uint8_t query_every = 2; // query every 2nd pattern by default
         uint64_t total_patterns_per_segment = std::round((query_seg_len - l + 1) / (double) query_every);
         double total_patterns_p = std::min(1.0, pattern_p * total_patterns_per_segment);
-        std::cout << "total_patterns_p\t" << total_patterns_p << '\n';
         return total_patterns_p;
     }
 
@@ -114,8 +155,8 @@ struct filtering_request
     uint64_t max_segment_len(param_set const & params) const
     {
         double pattern_p = pattern_spurious_match_prob(params);
-        size_t max_independent_patterns_per_segment = std::round(1.0f / pattern_p) - 1;
-        return l * max_independent_patterns_per_segment;
+        size_t max_patterns_per_segment = std::round(1.0 / pattern_p) - 1;
+        return l + query_every * (std::max(max_patterns_per_segment, (size_t) 2) - 1);
     }
 };
 
diff --git a/include/utilities/threshold/find.hpp b/include/utilities/threshold/find.hpp
index 769234b9..d1351418 100755
--- a/include/utilities/threshold/find.hpp
+++ b/include/utilities/threshold/find.hpp
@@ -22,18 +22,17 @@ param_set get_best_params(param_space const & space,
 /**
  * @brief For a chosen kmer size and error rate find the best threshold. 
 */
-uint8_t find_threshold(param_space const & space, 
-                      metadata const & ref_meta,
-                      metadata const & query_meta,
-                      split_arguments const & arguments,
-                      kmer_attributes const att);
+uint8_t find_heuristic_threshold(metadata const & ref_meta,
+                                 metadata const & query_meta, 
+                                 split_arguments const & arguments,
+                                 kmer_attributes const attr);
 
 /**
  * @brief For a chosen kmer size and some maximum error rate find the best threshold. 
 */
 void find_thresholds_for_kmer_size(param_space const & space, 
                                    metadata const & meta,
-                                   kmer_attributes const att, 
+                                   kmer_attributes const attr, 
                                    double const max_err);
 
 }   // namespace valik
diff --git a/include/utilities/threshold/kmer_attributes.hpp b/include/utilities/threshold/kmer_attributes.hpp
index 79d21332..e7a4e1bf 100755
--- a/include/utilities/threshold/kmer_attributes.hpp
+++ b/include/utilities/threshold/kmer_attributes.hpp
@@ -71,7 +71,9 @@ struct kmer_attributes
      * @brief False negative rate for a parameter set.
     */
     double fnr_for_param_set(filtering_request const & request, param_set const & params) const
-    {
+    {        
+        if (kmer_lemma_threshold(request.l, params.k, request.e) > 1)
+            return 0.0;
         return fn_conf_counts[params.t - 1][request.e][request.l] / (double) request.total_conf_count();
     }
 
diff --git a/include/utilities/threshold/param_set.hpp b/include/utilities/threshold/param_set.hpp
index 735f1f64..76f2222c 100755
--- a/include/utilities/threshold/param_set.hpp
+++ b/include/utilities/threshold/param_set.hpp
@@ -18,6 +18,7 @@ struct param_set
 
     param_set(uint8_t const kmer_size, uint8_t const thresh, param_space const & space) : k(kmer_size), t(thresh)
     {
+        /*
         if ((kmer_size < std::get<0>(space.kmer_range)) | (kmer_size > std::get<1>(space.kmer_range)))
         {
             throw std::runtime_error{"k=" + std::to_string(kmer_size) + " out of range [" + 
@@ -30,6 +31,7 @@ struct param_set
             throw std::runtime_error{"threshold=" + std::to_string(thresh) + " out of range [0, " + 
                                                            std::to_string(space.max_thresh) + "]"};
         }
+        */
     }
 };
 
diff --git a/src/argument_parsing/search.cpp b/src/argument_parsing/search.cpp
index 25527b7c..fb616aff 100644
--- a/src/argument_parsing/search.cpp
+++ b/src/argument_parsing/search.cpp
@@ -243,7 +243,6 @@ void run_search(sharg::parser & parser)
     if (kmer_lemma_threshold(arguments.pattern_size, (size_t) arguments.shape_size, (size_t) arguments.errors) <= 1)
     {
         //!TODO: read in parameter metadata file
-        arguments.threshold = 2;
         arguments.threshold_was_set = true;
     }
 
diff --git a/src/argument_parsing/split.cpp b/src/argument_parsing/split.cpp
index d0f0da44..ceb8409d 100644
--- a/src/argument_parsing/split.cpp
+++ b/src/argument_parsing/split.cpp
@@ -27,6 +27,11 @@ void init_split_parser(sharg::parser & parser, split_arguments & arguments)
                       .long_id = "error-rate",
                       .description = "Choose the upper bound for the maximum allowed error rate of a local match.",
                       .validator = sharg::arithmetic_range_validator{0.0f, 0.1f}});
+    parser.add_option(arguments.kmer_size,
+                      sharg::config{.short_id = 'k',
+                      .long_id = "kmer",
+                      .description = "Choose the kmer size.",
+                      .validator = positive_integer_validator{true}});
     parser.add_option(arguments.seg_count_in,
                       sharg::config{.short_id = 'n',
                       .long_id = "seg-count",
diff --git a/src/threshold/find.cpp b/src/threshold/find.cpp
index d37461eb..47b29c76 100755
--- a/src/threshold/find.cpp
+++ b/src/threshold/find.cpp
@@ -91,21 +91,22 @@ param_set get_best_params(param_space const & space,
 */
 void find_thresholds_for_kmer_size(param_space const & space, 
                                   metadata const & meta,
-                                  kmer_attributes const att, 
+                                  kmer_attributes const attr, 
                                   double const max_err)
 {
     std::cout.precision(3);
-    std::cout << "Recommended shared " << std::to_string(att.k) << "-mer thresholds for different error rates\n";
+    std::cout << "Recommended shared " << std::to_string(attr.k) << "-mer thresholds for different error rates\n";
     std::cout << "error_rate\tthreshold_kind\tthreshold\tFNR\tFP_per_pattern\tmax_query_seg_len\n";
 
-    auto best_params = param_set(att.k, space.max_thresh, space);
-    for (uint8_t errors{1}; errors < (meta.segment_overlap() * max_err); errors++)
+    auto best_params = param_set(attr.k, space.max_thresh, space);
+    for (uint8_t errors{1}; errors <= std::ceil(meta.segment_overlap() * max_err); errors++)
     {
         filtering_request request(errors, meta.segment_overlap(), meta.total_len, meta.seg_count);
         std::cout << errors / (double) request.l << '\t';
-        if (att.fnr_for_param_set(request, best_params) == 0)
+        if (kmer_lemma_threshold(request.l, attr.k, errors) > 1)
         {
-            std::cout << "kmer lemma\t" << std::to_string(kmer_lemma_threshold(request.l, att.k, errors)) << '\t' << 0;
+            best_params.t = kmer_lemma_threshold(request.l, attr.k, errors);
+            std::cout << "kmer lemma\t";
         }
         else
         {
@@ -113,55 +114,47 @@ void find_thresholds_for_kmer_size(param_space const & space,
             double best_score = request.l;
             for (uint8_t t{1}; t <= space.max_thresh; t++)
             {
-                auto params = param_set(att.k, t, space);
-                auto score = param_score(request, params, att);
+                auto params = param_set(attr.k, t, space);
+                auto score = param_score(request, params, attr);
                 if (score <= best_score)
                 {
                     best_params = params;
                     best_score = score;
                 }
             }
-            std::cout << std::to_string(best_params.t) << '\t' << att.fnr_for_param_set(request, best_params);
         }
 
-        std::cout << '\t' << request.pattern_spurious_match_prob(best_params) << '\t' << request.max_segment_len(best_params) << '\n';
+        std::cout << std::to_string(best_params.t) << '\t' << attr.fnr_for_param_set(request, best_params) << '\t'
+                  << request.pattern_spurious_match_prob(best_params) << '\n';
+                  // << request.max_segment_len(best_params) << '\n';
     }
 }
 
 /**
- * @brief For a chosen kmer size and error rate find the best threshold. 
+ * @brief For a chosen kmer size and error rate find the best heuristic threshold. 
 */
-uint8_t find_threshold(param_space const & space, 
-                       metadata const & ref_meta,
-                       metadata const & query_meta,
-                       split_arguments const & arguments,
-                       kmer_attributes const att)
+uint8_t find_heuristic_threshold(metadata const & ref_meta,
+                                 metadata const & query_meta,
+                                 split_arguments const & arguments,
+                                 kmer_attributes const attr)
 {
-
+    param_space space;
     filtering_request request(arguments.errors, arguments.pattern_size, ref_meta.total_len, ref_meta.seg_count);
-    auto best_params = param_set(arguments.kmer_size, space.max_thresh, space);
+    auto best_thresh = space.max_thresh;
     double best_score = arguments.pattern_size;
     for (uint8_t t{1}; t <= space.max_thresh; t++)
     {
-        auto params = param_set(att.k, t, space);
-        auto score = param_score(request, params, att);
+        auto params = param_set(arguments.kmer_size, t, space);
+        auto score = param_score(request, params, attr); 
+        
         if (score <= best_score)
         {
-            best_params = params;
+            best_thresh = params.t;
             best_score = score;
         }
-    }
-
-    std::cout.precision(3);
-    if (arguments.verbose)
-    {
-        std::cout << "threshold " << std::to_string(best_params.t) << '\n';
-        std::cout << "FNR " <<  att.fnr_for_param_set(request, best_params) << '\n';
-        std::cout << "segment len " << std::to_string(std::round(query_meta.total_len / (double) query_meta.seg_count)) << '\n';
-        std::cout << "FPR " << request.fpr(best_params, std::round(query_meta.total_len / (double) query_meta.seg_count)) << '\n';
-    }
+    }   
 
-    return best_params.t;
+    return best_thresh;
 }
 
 }   // namespace valik
diff --git a/src/valik_split.cpp b/src/valik_split.cpp
index fd997816..4b4e747e 100644
--- a/src/valik_split.cpp
+++ b/src/valik_split.cpp
@@ -28,43 +28,61 @@ void valik_split(split_arguments & arguments)
         if (!read_fn_confs(attr_vec))
             precalc_fn_confs(attr_vec);
 
+        filtering_request request(arguments.errors, arguments.pattern_size, meta.total_len, meta.seg_count);
         if (arguments.split_index)
         {
-            filtering_request request(arguments.errors, arguments.pattern_size, meta.total_len, meta.seg_count);
             auto best_params = get_best_params(space, request, attr_vec);
             arguments.kmer_size = best_params.k;
+            kmer_attributes attr = attr_vec[arguments.kmer_size - std::get<0>(space.kmer_range)];
 
             if (arguments.verbose)
             {
-                std::cout << "Build index for:\n";
+                std::cout << "\n-----------Index build parameters-----------\n";
                 std::cout << "db length " << meta.total_len << "bp\n";
                 std::cout << "min local match length " << arguments.pattern_size << "bp\n";
                 std::cout << "max error rate " << arguments.error_rate << "\n";
                 std::cout << "kmer size " << std::to_string(arguments.kmer_size) << '\n';
     
-                find_thresholds_for_kmer_size(space, meta, attr_vec[best_params.k - std::get<0>(space.kmer_range)], arguments.error_rate);
+                find_thresholds_for_kmer_size(space, meta, attr, arguments.error_rate);
             }
         }
         else
         {
-            if (kmer_lemma_threshold(arguments.pattern_size, (size_t) arguments.kmer_size, (size_t) arguments.errors) <= 1)
+            kmer_attributes attr = attr_vec[arguments.kmer_size - std::get<0>(space.kmer_range)];
+            auto best_threshold = kmer_lemma_threshold(arguments.pattern_size, (size_t) arguments.kmer_size, (size_t) arguments.errors);
+            if (arguments.verbose)
             {
-                metadata ref_meta = metadata(arguments.ref_meta_path);
-                auto best_threshold = find_threshold(space, ref_meta, meta, arguments, attr_vec[arguments.kmer_size - std::get<0>(space.kmer_range)]); 
+                std::cout.precision(3);
+                std::cout << "\n-----------Search parameters-----------\n";
+                std::cout << "segment len " << std::to_string((uint64_t) std::round(meta.total_len / (double) meta.seg_count)) << '\n';
+                std::cout << "min local match length " << arguments.pattern_size << "bp\n";
+                std::cout << "error rate " << arguments.error_rate << "\n";
+                std::cout << "kmer size " << std::to_string(arguments.kmer_size) << '\n';
+            }
+            
+            metadata ref_meta = metadata(arguments.ref_meta_path);
+            if (best_threshold <= 1)
+            {
+                best_threshold = find_heuristic_threshold(ref_meta, meta, arguments, attr); 
                 if (arguments.verbose)
                 {
-                    std::cout.precision(3);
-                    std::cout << "Can not search database with an exact k-mer lemma threshold with parameters\n";
-                    std::cout << "min local match length " << arguments.pattern_size << "bp\n";
-                    std::cout << "error rate " << arguments.error_rate << "\n";
-                    std::cout << "kmer size " << std::to_string(arguments.kmer_size) << '\n';
-
-                    std::cout << "Applying heuristic threshold\n";
-                    std::cout << "use threshold " << best_threshold;
+                    std::cout << "Apply heuristic threshold ";
                 }
             }
-        }
+            else
+            {
+                if (arguments.verbose)
+                    std::cout << "Use k-mer lemma threshold ";
+            }
 
+            if (arguments.verbose)
+            {
+                param_set best_params(arguments.kmer_size, best_threshold, space);
+                std::cout << best_threshold << '\n';
+                std::cout << "FNR " <<  attr.fnr_for_param_set(request, best_params) << '\n';
+                std::cout << "FPR " << request.fpr(best_params, std::round(meta.total_len / (double) meta.seg_count), ref_meta.total_len, ref_meta.seg_count) << '\n';
+            }
+        }
     }
 
     if (arguments.write_out)